exp_first_half – Complete Experiment Report
Base_Gaussian
(MvNormal,
mu,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
-0.537 |
0.594 |
-0.165 |
| SMC |
(0.0, 0.0) |
0.020 |
0.984 |
0.008 |
| Metro |
(0.0, 0.0) |
2.980 |
0.00561 |
1.326 |
| DEMetro_Z |
(0.0, 0.0) |
3.865 |
0.000571 |
1.819 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-4.373
|
0.000327
|
-0.978
|
| Metro_vs_SMC |
0
|
2.511
|
0.0213
|
0.561
|
| Metro_vs_DEMetro_Z |
0
|
-0.904
|
0.378
|
-0.202
|
| HMC_vs_Metro |
0
|
-3.323
|
0.00358
|
-0.743
|
| HMC_vs_SMC |
0
|
-0.549
|
0.589
|
-0.123
|
| DEMetro_Z_vs_SMC |
0
|
3.702
|
0.00151
|
0.828
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.021 |
0.022 |
0.010 |
-0.165 |
| SMC |
(0.0, 0.0) |
0.022 |
0.022 |
0.010 |
0.008 |
| Metro |
(0.0, 0.0) |
0.035 |
0.022 |
0.010 |
1.326 |
| DEMetro_Z |
(0.0, 0.0) |
0.040 |
0.022 |
0.010 |
1.819 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
0.202 |
0.841 |
0.068 |
| SMC |
(0.0, 0.0) |
0.125 |
0.901 |
0.042 |
| Metro |
(0.0, 0.0) |
1.536 |
0.133 |
0.553 |
| DEMetro_Z |
(0.0, 0.0) |
3.258 |
0.00291 |
1.597 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.071
|
0.944
|
0.016
|
| Metro_vs_DEMetro_Z |
0
|
-2.059
|
0.0535
|
-0.460
|
| HMC_vs_Metro |
0
|
-1.950
|
0.0661
|
-0.436
|
| HMC_vs_DEMetro_Z |
0
|
-3.826
|
0.00114
|
-0.856
|
| Metro_vs_SMC |
0
|
1.233
|
0.232
|
0.276
|
| DEMetro_Z_vs_SMC |
0
|
3.102
|
0.00587
|
0.694
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.032 |
0.031 |
0.016 |
0.068 |
| SMC |
(0.0, 0.0) |
0.031 |
0.031 |
0.016 |
0.042 |
| Metro |
(0.0, 0.0) |
0.040 |
0.031 |
0.016 |
0.553 |
| DEMetro_Z |
(0.0, 0.0) |
0.056 |
0.031 |
0.016 |
1.597 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
-0.385 |
0.702 |
-0.140 |
| SMC |
(0.0, 0.0) |
0.095 |
0.925 |
0.043 |
| Metro |
(0.0, 0.0) |
4.788 |
5.65e-05 |
2.600 |
| DEMetro_Z |
(0.0, 0.0) |
8.376 |
1.02e-08 |
5.030 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.624
|
0.0018
|
-0.810
|
| DEMetro_Z_vs_SMC |
0
|
7.507
|
4.25e-07
|
1.679
|
| HMC_vs_DEMetro_Z |
0
|
-8.512
|
6.59e-08
|
-1.903
|
| HMC_vs_Metro |
0
|
-5.036
|
7.34e-05
|
-1.126
|
| HMC_vs_SMC |
0
|
-0.491
|
0.629
|
-0.110
|
| Metro_vs_SMC |
0
|
3.547
|
0.00215
|
0.793
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.030 |
0.030 |
0.005 |
-0.140 |
| SMC |
(0.0, 0.0) |
0.031 |
0.030 |
0.005 |
0.043 |
| Metro |
(0.0, 0.0) |
0.043 |
0.030 |
0.005 |
2.600 |
| DEMetro_Z |
(0.0, 0.0) |
0.055 |
0.030 |
0.005 |
5.030 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
-0.480 |
0.634 |
-0.155 |
| SMC |
(0.0, 0.0) |
0.109 |
0.914 |
0.045 |
| Metro |
(0.0, 0.0) |
4.130 |
0.000249 |
1.775 |
| DEMetro_Z |
(0.0, 0.0) |
6.247 |
1.27e-06 |
3.451 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.267
|
4.39e-05
|
1.178
|
| HMC_vs_Metro |
0
|
-4.372
|
0.000328
|
-0.978
|
| Metro_vs_DEMetro_Z |
0
|
-2.880
|
0.0096
|
-0.644
|
| HMC_vs_SMC |
0
|
-0.623
|
0.54
|
-0.139
|
| Metro_vs_SMC |
0
|
2.967
|
0.00792
|
0.663
|
| HMC_vs_DEMetro_Z |
0
|
-6.765
|
1.84e-06
|
-1.513
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.014 |
0.015 |
0.004 |
-0.155 |
| SMC |
(0.0, 0.0) |
0.015 |
0.015 |
0.004 |
0.045 |
| Metro |
(0.0, 0.0) |
0.021 |
0.015 |
0.004 |
1.775 |
| DEMetro_Z |
(0.0, 0.0) |
0.027 |
0.015 |
0.004 |
3.451 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
-0.608 |
0.547 |
-0.215 |
| SMC |
(0.0, 0.0) |
-0.472 |
0.64 |
-0.184 |
| Metro |
(0.0, 0.0) |
3.288 |
0.00259 |
1.503 |
| DEMetro_Z |
(0.0, 0.0) |
3.985 |
0.000512 |
2.375 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-5.045
|
7.19e-05
|
-1.128
|
| Metro_vs_SMC |
0
|
3.579
|
0.002
|
0.800
|
| Metro_vs_DEMetro_Z |
0
|
-1.307
|
0.207
|
-0.292
|
| HMC_vs_Metro |
0
|
-3.514
|
0.00232
|
-0.786
|
| HMC_vs_SMC |
0
|
-0.094
|
0.926
|
-0.021
|
| DEMetro_Z_vs_SMC |
0
|
4.193
|
0.000493
|
0.938
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.020 |
0.022 |
0.010 |
-0.215 |
| SMC |
(0.0, 0.0) |
0.021 |
0.022 |
0.010 |
-0.184 |
| Metro |
(0.0, 0.0) |
0.037 |
0.022 |
0.010 |
1.503 |
| DEMetro_Z |
(0.0, 0.0) |
0.045 |
0.022 |
0.010 |
2.375 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
0.594 |
0.556 |
0.179 |
| SMC |
(0.0, 0.0) |
-1.040 |
0.306 |
-0.291 |
| Metro |
(0.0, 0.0) |
2.921 |
0.00656 |
1.329 |
| DEMetro_Z |
(0.0, 0.0) |
3.988 |
0.00037 |
1.711 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.683
|
0.109
|
0.376
|
| Metro_vs_DEMetro_Z |
0
|
-0.800
|
0.434
|
-0.179
|
| HMC_vs_Metro |
0
|
-2.504
|
0.0215
|
-0.560
|
| HMC_vs_DEMetro_Z |
0
|
-3.150
|
0.00527
|
-0.704
|
| Metro_vs_SMC |
0
|
3.535
|
0.00221
|
0.790
|
| DEMetro_Z_vs_SMC |
0
|
5.032
|
7.41e-05
|
1.125
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.034 |
0.031 |
0.016 |
0.179 |
| SMC |
(0.0, 0.0) |
0.026 |
0.031 |
0.016 |
-0.291 |
| Metro |
(0.0, 0.0) |
0.052 |
0.031 |
0.016 |
1.329 |
| DEMetro_Z |
(0.0, 0.0) |
0.058 |
0.031 |
0.016 |
1.711 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
0.045 |
0.964 |
0.016 |
| SMC |
(0.0, 0.0) |
-0.318 |
0.753 |
-0.145 |
| Metro |
(0.0, 0.0) |
4.457 |
0.000174 |
3.083 |
| DEMetro_Z |
(0.0, 0.0) |
6.441 |
1.9e-06 |
5.618 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.565
|
0.0189
|
-0.574
|
| DEMetro_Z_vs_SMC |
0
|
6.420
|
3.73e-06
|
1.436
|
| HMC_vs_DEMetro_Z |
0
|
-7.432
|
4.92e-07
|
-1.662
|
| HMC_vs_Metro |
0
|
-4.319
|
0.00037
|
-0.966
|
| HMC_vs_SMC |
0
|
0.387
|
0.703
|
0.086
|
| Metro_vs_SMC |
0
|
4.600
|
0.000196
|
1.028
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.031 |
0.030 |
0.005 |
0.016 |
| SMC |
(0.0, 0.0) |
0.030 |
0.030 |
0.005 |
-0.145 |
| Metro |
(0.0, 0.0) |
0.045 |
0.030 |
0.005 |
3.083 |
| DEMetro_Z |
(0.0, 0.0) |
0.058 |
0.030 |
0.005 |
5.618 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
(0.0, 0.0) |
-0.086 |
0.932 |
-0.030 |
| SMC |
(0.0, 0.0) |
-0.421 |
0.677 |
-0.166 |
| Metro |
(0.0, 0.0) |
4.135 |
0.000345 |
2.439 |
| DEMetro_Z |
(0.0, 0.0) |
5.346 |
1.93e-05 |
3.764 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.379
|
3.44e-05
|
1.203
|
| HMC_vs_Metro |
0
|
-4.003
|
0.00076
|
-0.895
|
| Metro_vs_DEMetro_Z |
0
|
-1.774
|
0.0921
|
-0.397
|
| HMC_vs_SMC |
0
|
0.339
|
0.739
|
0.076
|
| Metro_vs_SMC |
0
|
4.415
|
0.000298
|
0.987
|
| HMC_vs_DEMetro_Z |
0
|
-6.140
|
6.68e-06
|
-1.373
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
(0.0, 0.0) |
0.015 |
0.015 |
0.004 |
-0.030 |
| SMC |
(0.0, 0.0) |
0.014 |
0.015 |
0.004 |
-0.166 |
| Metro |
(0.0, 0.0) |
0.024 |
0.015 |
0.004 |
2.439 |
| DEMetro_Z |
(0.0, 0.0) |
0.029 |
0.015 |
0.004 |
3.764 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_only_Correlation
(MvNormal,
correlation,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.052 |
0.959 |
0.016 |
| HMC |
0.3 |
1.300 |
0.202 |
0.375 |
| HMC |
0.5 |
1.884 |
0.0686 |
0.787 |
| HMC |
0.9 |
1.441 |
0.16 |
0.647 |
| HMC |
0.99 |
3.119 |
0.00398 |
1.415 |
| SMC |
0.0 |
-1.261 |
0.215 |
-0.403 |
| SMC |
0.3 |
0.560 |
0.579 |
0.162 |
| SMC |
0.5 |
0.190 |
0.85 |
0.072 |
| SMC |
0.9 |
-0.737 |
0.465 |
-0.244 |
| SMC |
0.99 |
-0.675 |
0.503 |
-0.215 |
| Metro |
0.0 |
3.790 |
0.000674 |
1.713 |
| Metro |
0.3 |
4.647 |
4.68e-05 |
1.759 |
| Metro |
0.5 |
3.126 |
0.00464 |
2.106 |
| Metro |
0.9 |
4.476 |
0.000221 |
5.254 |
| Metro |
0.99 |
4.343 |
0.000344 |
15.396 |
| DEMetro_Z |
0.0 |
2.900 |
0.00744 |
1.589 |
| DEMetro_Z |
0.3 |
3.060 |
0.00525 |
1.858 |
| DEMetro_Z |
0.5 |
4.325 |
0.000222 |
2.690 |
| DEMetro_Z |
0.9 |
2.984 |
0.00517 |
1.130 |
| DEMetro_Z |
0.99 |
1.966 |
0.0594 |
0.984 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-3.414
|
0.00291
|
-0.763
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.534
|
0.0202
|
-0.567
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.828
|
0.0107
|
-0.632
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.889
|
0.385
|
-0.199
|
| HMC_vs_DEMetro_Z |
0.99
|
0.679
|
0.505
|
0.152
|
| Metro_vs_SMC |
0.0
|
4.735
|
0.000144
|
1.059
|
| Metro_vs_SMC |
0.3
|
4.414
|
0.000298
|
0.987
|
| Metro_vs_SMC |
0.5
|
2.707
|
0.014
|
0.605
|
| Metro_vs_SMC |
0.9
|
4.421
|
0.000293
|
0.989
|
| Metro_vs_SMC |
0.99
|
4.515
|
0.000237
|
1.010
|
| Metro_vs_DEMetro_Z |
0.0
|
0.219
|
0.829
|
0.049
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.140
|
0.89
|
-0.031
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.740
|
0.469
|
-0.165
|
| Metro_vs_DEMetro_Z |
0.9
|
3.097
|
0.00593
|
0.693
|
| Metro_vs_DEMetro_Z |
0.99
|
3.983
|
0.000797
|
0.891
|
| HMC_vs_Metro |
0.0
|
-4.067
|
0.000657
|
-0.909
|
| HMC_vs_Metro |
0.3
|
-4.947
|
8.94e-05
|
-1.106
|
| HMC_vs_Metro |
0.5
|
-1.778
|
0.0915
|
-0.397
|
| HMC_vs_Metro |
0.9
|
-4.033
|
0.00071
|
-0.902
|
| HMC_vs_Metro |
0.99
|
-4.050
|
0.000683
|
-0.906
|
| HMC_vs_SMC |
0.0
|
2.165
|
0.0433
|
0.484
|
| HMC_vs_SMC |
0.3
|
0.864
|
0.398
|
0.193
|
| HMC_vs_SMC |
0.5
|
2.009
|
0.0589
|
0.449
|
| HMC_vs_SMC |
0.9
|
1.904
|
0.0722
|
0.426
|
| HMC_vs_SMC |
0.99
|
3.769
|
0.0013
|
0.843
|
| DEMetro_Z_vs_SMC |
0.0
|
4.204
|
0.000481
|
0.940
|
| DEMetro_Z_vs_SMC |
0.3
|
2.861
|
0.01
|
0.640
|
| DEMetro_Z_vs_SMC |
0.5
|
4.370
|
0.000329
|
0.977
|
| DEMetro_Z_vs_SMC |
0.9
|
3.216
|
0.00455
|
0.719
|
| DEMetro_Z_vs_SMC |
0.99
|
2.174
|
0.0425
|
0.486
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.022 |
0.022 |
0.010 |
0.016 |
| HMC |
0.3 |
0.021 |
0.017 |
0.011 |
0.375 |
| HMC |
0.5 |
0.025 |
0.019 |
0.008 |
0.787 |
| HMC |
0.9 |
0.027 |
0.020 |
0.012 |
0.647 |
| HMC |
0.99 |
0.035 |
0.018 |
0.012 |
1.415 |
| SMC |
0.0 |
0.018 |
0.022 |
0.010 |
-0.403 |
| SMC |
0.3 |
0.019 |
0.017 |
0.011 |
0.162 |
| SMC |
0.5 |
0.019 |
0.019 |
0.008 |
0.072 |
| SMC |
0.9 |
0.017 |
0.020 |
0.012 |
-0.244 |
| SMC |
0.99 |
0.016 |
0.018 |
0.012 |
-0.215 |
| Metro |
0.0 |
0.039 |
0.022 |
0.010 |
1.713 |
| Metro |
0.3 |
0.037 |
0.017 |
0.011 |
1.759 |
| Metro |
0.5 |
0.035 |
0.019 |
0.008 |
2.106 |
| Metro |
0.9 |
0.081 |
0.020 |
0.012 |
5.254 |
| Metro |
0.99 |
0.202 |
0.018 |
0.012 |
15.396 |
| DEMetro_Z |
0.0 |
0.038 |
0.022 |
0.010 |
1.589 |
| DEMetro_Z |
0.3 |
0.038 |
0.017 |
0.011 |
1.858 |
| DEMetro_Z |
0.5 |
0.040 |
0.019 |
0.008 |
2.690 |
| DEMetro_Z |
0.9 |
0.033 |
0.020 |
0.012 |
1.130 |
| DEMetro_Z |
0.99 |
0.030 |
0.018 |
0.012 |
0.984 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.656 |
0.516 |
-0.191 |
| HMC |
0.3 |
0.575 |
0.569 |
0.191 |
| HMC |
0.5 |
0.565 |
0.575 |
0.198 |
| HMC |
0.9 |
1.772 |
0.0881 |
0.989 |
| HMC |
0.99 |
3.090 |
0.00436 |
1.452 |
| SMC |
0.0 |
-0.412 |
0.683 |
-0.137 |
| SMC |
0.3 |
0.666 |
0.509 |
0.208 |
| SMC |
0.5 |
1.094 |
0.282 |
0.432 |
| SMC |
0.9 |
-0.618 |
0.54 |
-0.212 |
| SMC |
0.99 |
0.409 |
0.685 |
0.164 |
| Metro |
0.0 |
1.504 |
0.141 |
0.550 |
| Metro |
0.3 |
3.339 |
0.00233 |
1.601 |
| Metro |
0.5 |
4.548 |
7.61e-05 |
1.951 |
| Metro |
0.9 |
3.619 |
0.0015 |
2.899 |
| Metro |
0.99 |
5.747 |
1.4e-05 |
11.476 |
| DEMetro_Z |
0.0 |
3.519 |
0.00116 |
1.202 |
| DEMetro_Z |
0.3 |
3.685 |
0.00104 |
2.008 |
| DEMetro_Z |
0.5 |
4.677 |
0.000108 |
3.508 |
| DEMetro_Z |
0.9 |
2.011 |
0.054 |
0.999 |
| DEMetro_Z |
0.99 |
2.201 |
0.0365 |
1.163 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-0.167
|
0.869
|
-0.037
|
| HMC_vs_SMC |
0.3
|
-0.054
|
0.958
|
-0.012
|
| HMC_vs_SMC |
0.5
|
-0.730
|
0.474
|
-0.163
|
| HMC_vs_SMC |
0.9
|
1.830
|
0.0829
|
0.409
|
| HMC_vs_SMC |
0.99
|
2.359
|
0.0292
|
0.528
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.873
|
0.0765
|
-0.419
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.532
|
0.601
|
-0.119
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.713
|
0.103
|
-0.383
|
| Metro_vs_DEMetro_Z |
0.9
|
1.917
|
0.0703
|
0.429
|
| Metro_vs_DEMetro_Z |
0.99
|
4.769
|
0.000133
|
1.066
|
| HMC_vs_Metro |
0.0
|
-2.620
|
0.0168
|
-0.586
|
| HMC_vs_Metro |
0.3
|
-3.017
|
0.00709
|
-0.675
|
| HMC_vs_Metro |
0.5
|
-4.763
|
0.000135
|
-1.065
|
| HMC_vs_Metro |
0.9
|
-1.994
|
0.0607
|
-0.446
|
| HMC_vs_Metro |
0.99
|
-4.940
|
9.09e-05
|
-1.105
|
| HMC_vs_DEMetro_Z |
0.0
|
-4.439
|
0.000281
|
-0.993
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.094
|
0.000618
|
-0.915
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.833
|
0.000116
|
-1.081
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.012
|
0.99
|
-0.003
|
| HMC_vs_DEMetro_Z |
0.99
|
0.482
|
0.635
|
0.108
|
| Metro_vs_SMC |
0.0
|
2.051
|
0.0543
|
0.459
|
| Metro_vs_SMC |
0.3
|
2.938
|
0.00844
|
0.657
|
| Metro_vs_SMC |
0.5
|
4.036
|
0.000706
|
0.902
|
| Metro_vs_SMC |
0.9
|
3.526
|
0.00226
|
0.788
|
| Metro_vs_SMC |
0.99
|
5.606
|
2.09e-05
|
1.253
|
| DEMetro_Z_vs_SMC |
0.0
|
3.180
|
0.00493
|
0.711
|
| DEMetro_Z_vs_SMC |
0.3
|
3.916
|
0.000929
|
0.876
|
| DEMetro_Z_vs_SMC |
0.5
|
3.969
|
0.000822
|
0.888
|
| DEMetro_Z_vs_SMC |
0.9
|
2.832
|
0.0106
|
0.633
|
| DEMetro_Z_vs_SMC |
0.99
|
1.597
|
0.127
|
0.357
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.028 |
0.031 |
0.016 |
-0.191 |
| HMC |
0.3 |
0.029 |
0.026 |
0.014 |
0.191 |
| HMC |
0.5 |
0.028 |
0.026 |
0.012 |
0.198 |
| HMC |
0.9 |
0.048 |
0.033 |
0.015 |
0.989 |
| HMC |
0.99 |
0.053 |
0.026 |
0.018 |
1.452 |
| SMC |
0.0 |
0.028 |
0.031 |
0.016 |
-0.137 |
| SMC |
0.3 |
0.029 |
0.026 |
0.014 |
0.208 |
| SMC |
0.5 |
0.031 |
0.026 |
0.012 |
0.432 |
| SMC |
0.9 |
0.029 |
0.033 |
0.015 |
-0.212 |
| SMC |
0.99 |
0.029 |
0.026 |
0.018 |
0.164 |
| Metro |
0.0 |
0.040 |
0.031 |
0.016 |
0.550 |
| Metro |
0.3 |
0.049 |
0.026 |
0.014 |
1.601 |
| Metro |
0.5 |
0.050 |
0.026 |
0.012 |
1.951 |
| Metro |
0.9 |
0.078 |
0.033 |
0.015 |
2.899 |
| Metro |
0.99 |
0.234 |
0.026 |
0.018 |
11.476 |
| DEMetro_Z |
0.0 |
0.050 |
0.031 |
0.016 |
1.202 |
| DEMetro_Z |
0.3 |
0.054 |
0.026 |
0.014 |
2.008 |
| DEMetro_Z |
0.5 |
0.069 |
0.026 |
0.012 |
3.508 |
| DEMetro_Z |
0.9 |
0.048 |
0.033 |
0.015 |
0.999 |
| DEMetro_Z |
0.99 |
0.047 |
0.026 |
0.018 |
1.163 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.326 |
0.746 |
0.112 |
| HMC |
0.3 |
1.153 |
0.256 |
0.357 |
| HMC |
0.5 |
2.001 |
0.0543 |
0.882 |
| HMC |
0.9 |
2.613 |
0.0141 |
1.245 |
| HMC |
0.99 |
5.161 |
1.46e-05 |
2.334 |
| SMC |
0.0 |
-1.656 |
0.107 |
-0.613 |
| SMC |
0.3 |
0.450 |
0.655 |
0.132 |
| SMC |
0.5 |
0.649 |
0.521 |
0.244 |
| SMC |
0.9 |
-0.055 |
0.956 |
-0.019 |
| SMC |
0.99 |
-0.267 |
0.791 |
-0.092 |
| Metro |
0.0 |
5.244 |
1.78e-05 |
2.946 |
| Metro |
0.3 |
6.565 |
2.16e-07 |
2.764 |
| Metro |
0.5 |
5.574 |
9.01e-06 |
3.450 |
| Metro |
0.9 |
5.599 |
1.73e-05 |
7.448 |
| Metro |
0.99 |
6.665 |
2.19e-06 |
28.081 |
| DEMetro_Z |
0.0 |
7.322 |
1.22e-07 |
4.489 |
| DEMetro_Z |
0.3 |
5.782 |
5.67e-06 |
3.702 |
| DEMetro_Z |
0.5 |
8.335 |
9.84e-09 |
4.857 |
| DEMetro_Z |
0.9 |
6.043 |
7.78e-07 |
2.377 |
| DEMetro_Z |
0.99 |
5.212 |
1.64e-05 |
2.676 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-2.297
|
0.0332
|
-0.514
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.224
|
0.236
|
-0.274
|
| Metro_vs_DEMetro_Z |
0.5
|
-2.079
|
0.0514
|
-0.465
|
| Metro_vs_DEMetro_Z |
0.9
|
3.372
|
0.0032
|
0.754
|
| Metro_vs_DEMetro_Z |
0.99
|
5.970
|
9.58e-06
|
1.335
|
| DEMetro_Z_vs_SMC |
0.0
|
8.578
|
5.85e-08
|
1.918
|
| DEMetro_Z_vs_SMC |
0.3
|
6.060
|
7.91e-06
|
1.355
|
| DEMetro_Z_vs_SMC |
0.5
|
7.636
|
3.32e-07
|
1.708
|
| DEMetro_Z_vs_SMC |
0.9
|
5.535
|
2.44e-05
|
1.238
|
| DEMetro_Z_vs_SMC |
0.99
|
4.396
|
0.000311
|
0.983
|
| HMC_vs_DEMetro_Z |
0.0
|
-6.836
|
1.59e-06
|
-1.529
|
| HMC_vs_DEMetro_Z |
0.3
|
-5.670
|
1.82e-05
|
-1.268
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.695
|
1.72e-05
|
-1.274
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.033
|
0.0563
|
-0.455
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.550
|
0.589
|
-0.123
|
| HMC_vs_Metro |
0.0
|
-5.312
|
3.98e-05
|
-1.188
|
| HMC_vs_Metro |
0.3
|
-6.311
|
4.67e-06
|
-1.411
|
| HMC_vs_Metro |
0.5
|
-3.630
|
0.00178
|
-0.812
|
| HMC_vs_Metro |
0.9
|
-5.137
|
5.86e-05
|
-1.149
|
| HMC_vs_Metro |
0.99
|
-6.216
|
5.69e-06
|
-1.390
|
| HMC_vs_SMC |
0.0
|
2.218
|
0.0389
|
0.496
|
| HMC_vs_SMC |
0.3
|
0.768
|
0.452
|
0.172
|
| HMC_vs_SMC |
0.5
|
1.656
|
0.114
|
0.370
|
| HMC_vs_SMC |
0.9
|
2.215
|
0.0392
|
0.495
|
| HMC_vs_SMC |
0.99
|
4.625
|
0.000185
|
1.034
|
| Metro_vs_SMC |
0.0
|
6.041
|
8.23e-06
|
1.351
|
| Metro_vs_SMC |
0.3
|
6.348
|
4.32e-06
|
1.420
|
| Metro_vs_SMC |
0.5
|
4.633
|
0.000181
|
1.036
|
| Metro_vs_SMC |
0.9
|
5.450
|
2.94e-05
|
1.219
|
| Metro_vs_SMC |
0.99
|
6.715
|
2.03e-06
|
1.502
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.031 |
0.030 |
0.005 |
0.112 |
| HMC |
0.3 |
0.029 |
0.027 |
0.007 |
0.357 |
| HMC |
0.5 |
0.033 |
0.028 |
0.006 |
0.882 |
| HMC |
0.9 |
0.037 |
0.028 |
0.008 |
1.245 |
| HMC |
0.99 |
0.043 |
0.025 |
0.008 |
2.334 |
| SMC |
0.0 |
0.028 |
0.030 |
0.005 |
-0.613 |
| SMC |
0.3 |
0.028 |
0.027 |
0.007 |
0.132 |
| SMC |
0.5 |
0.029 |
0.028 |
0.006 |
0.244 |
| SMC |
0.9 |
0.028 |
0.028 |
0.008 |
-0.019 |
| SMC |
0.99 |
0.025 |
0.025 |
0.008 |
-0.092 |
| Metro |
0.0 |
0.045 |
0.030 |
0.005 |
2.946 |
| Metro |
0.3 |
0.045 |
0.027 |
0.007 |
2.764 |
| Metro |
0.5 |
0.047 |
0.028 |
0.006 |
3.450 |
| Metro |
0.9 |
0.084 |
0.028 |
0.008 |
7.448 |
| Metro |
0.99 |
0.241 |
0.025 |
0.008 |
28.081 |
| DEMetro_Z |
0.0 |
0.052 |
0.030 |
0.005 |
4.489 |
| DEMetro_Z |
0.3 |
0.051 |
0.027 |
0.007 |
3.702 |
| DEMetro_Z |
0.5 |
0.055 |
0.028 |
0.006 |
4.857 |
| DEMetro_Z |
0.9 |
0.046 |
0.028 |
0.008 |
2.377 |
| DEMetro_Z |
0.99 |
0.046 |
0.025 |
0.008 |
2.676 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.238 |
0.813 |
-0.069 |
| HMC |
0.3 |
0.741 |
0.464 |
0.241 |
| HMC |
0.5 |
2.112 |
0.042 |
0.820 |
| HMC |
0.9 |
2.114 |
0.0419 |
0.827 |
| HMC |
0.99 |
4.877 |
2.13e-05 |
1.732 |
| SMC |
0.0 |
-1.369 |
0.18 |
-0.515 |
| SMC |
0.3 |
0.377 |
0.708 |
0.113 |
| SMC |
0.5 |
0.544 |
0.59 |
0.192 |
| SMC |
0.9 |
-0.021 |
0.983 |
-0.006 |
| SMC |
0.99 |
-0.951 |
0.348 |
-0.329 |
| Metro |
0.0 |
4.366 |
0.000167 |
2.289 |
| Metro |
0.3 |
5.825 |
1.65e-06 |
2.373 |
| Metro |
0.5 |
5.139 |
2.2e-05 |
2.776 |
| Metro |
0.9 |
5.472 |
1.91e-05 |
5.185 |
| Metro |
0.99 |
8.357 |
7.89e-08 |
23.029 |
| DEMetro_Z |
0.0 |
5.719 |
4.12e-06 |
2.913 |
| DEMetro_Z |
0.3 |
4.359 |
0.000199 |
2.648 |
| DEMetro_Z |
0.5 |
7.399 |
5.46e-08 |
3.827 |
| DEMetro_Z |
0.9 |
4.727 |
3.74e-05 |
1.804 |
| DEMetro_Z |
0.99 |
3.570 |
0.00129 |
1.727 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
6.855
|
1.53e-06
|
1.533
|
| DEMetro_Z_vs_SMC |
0.3
|
4.705
|
0.000154
|
1.052
|
| DEMetro_Z_vs_SMC |
0.5
|
6.694
|
2.12e-06
|
1.497
|
| DEMetro_Z_vs_SMC |
0.9
|
4.873
|
0.000106
|
1.090
|
| DEMetro_Z_vs_SMC |
0.99
|
3.498
|
0.00241
|
0.782
|
| HMC_vs_Metro |
0.0
|
-5.759
|
1.5e-05
|
-1.288
|
| HMC_vs_Metro |
0.3
|
-5.400
|
3.28e-05
|
-1.207
|
| HMC_vs_Metro |
0.5
|
-3.552
|
0.00213
|
-0.794
|
| HMC_vs_Metro |
0.9
|
-4.630
|
0.000183
|
-1.035
|
| HMC_vs_Metro |
0.99
|
-7.817
|
2.36e-07
|
-1.748
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.954
|
0.352
|
-0.213
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.379
|
0.709
|
-0.085
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.766
|
0.0935
|
-0.395
|
| Metro_vs_DEMetro_Z |
0.9
|
3.105
|
0.00583
|
0.694
|
| Metro_vs_DEMetro_Z |
0.99
|
7.727
|
2.8e-07
|
1.728
|
| HMC_vs_SMC |
0.0
|
1.309
|
0.206
|
0.293
|
| HMC_vs_SMC |
0.3
|
0.449
|
0.658
|
0.101
|
| HMC_vs_SMC |
0.5
|
2.051
|
0.0543
|
0.459
|
| HMC_vs_SMC |
0.9
|
1.796
|
0.0884
|
0.402
|
| HMC_vs_SMC |
0.99
|
4.820
|
0.000119
|
1.078
|
| Metro_vs_SMC |
0.0
|
4.988
|
8.17e-05
|
1.115
|
| Metro_vs_SMC |
0.3
|
5.561
|
2.31e-05
|
1.243
|
| Metro_vs_SMC |
0.5
|
4.338
|
0.000354
|
0.970
|
| Metro_vs_SMC |
0.9
|
5.392
|
3.34e-05
|
1.206
|
| Metro_vs_SMC |
0.99
|
8.426
|
7.69e-08
|
1.884
|
| HMC_vs_DEMetro_Z |
0.0
|
-6.192
|
5.99e-06
|
-1.385
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.302
|
0.000384
|
-0.962
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.227
|
4.8e-05
|
-1.169
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.263
|
0.0355
|
-0.506
|
| HMC_vs_DEMetro_Z |
0.99
|
0.009
|
0.993
|
0.002
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.014 |
0.015 |
0.004 |
-0.069 |
| HMC |
0.3 |
0.014 |
0.013 |
0.005 |
0.241 |
| HMC |
0.5 |
0.017 |
0.014 |
0.004 |
0.820 |
| HMC |
0.9 |
0.020 |
0.015 |
0.006 |
0.827 |
| HMC |
0.99 |
0.023 |
0.014 |
0.005 |
1.732 |
| SMC |
0.0 |
0.013 |
0.015 |
0.004 |
-0.515 |
| SMC |
0.3 |
0.013 |
0.013 |
0.005 |
0.113 |
| SMC |
0.5 |
0.014 |
0.014 |
0.004 |
0.192 |
| SMC |
0.9 |
0.015 |
0.015 |
0.006 |
-0.006 |
| SMC |
0.99 |
0.013 |
0.014 |
0.005 |
-0.329 |
| Metro |
0.0 |
0.023 |
0.015 |
0.004 |
2.289 |
| Metro |
0.3 |
0.024 |
0.013 |
0.005 |
2.373 |
| Metro |
0.5 |
0.025 |
0.014 |
0.004 |
2.776 |
| Metro |
0.9 |
0.046 |
0.015 |
0.006 |
5.185 |
| Metro |
0.99 |
0.134 |
0.014 |
0.005 |
23.029 |
| DEMetro_Z |
0.0 |
0.025 |
0.015 |
0.004 |
2.913 |
| DEMetro_Z |
0.3 |
0.025 |
0.013 |
0.005 |
2.648 |
| DEMetro_Z |
0.5 |
0.029 |
0.014 |
0.004 |
3.827 |
| DEMetro_Z |
0.9 |
0.026 |
0.015 |
0.006 |
1.804 |
| DEMetro_Z |
0.99 |
0.023 |
0.014 |
0.005 |
1.727 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.294 |
0.771 |
0.106 |
| HMC |
0.3 |
1.153 |
0.256 |
0.407 |
| HMC |
0.5 |
1.440 |
0.16 |
0.639 |
| HMC |
0.9 |
1.459 |
0.153 |
0.534 |
| HMC |
0.99 |
2.800 |
0.00932 |
1.464 |
| SMC |
0.0 |
-0.814 |
0.421 |
-0.263 |
| SMC |
0.3 |
-0.012 |
0.99 |
-0.004 |
| SMC |
0.5 |
0.271 |
0.788 |
0.095 |
| SMC |
0.9 |
-1.118 |
0.271 |
-0.376 |
| SMC |
0.99 |
-3.410 |
0.00197 |
-0.857 |
| Metro |
0.0 |
2.098 |
0.0436 |
0.843 |
| Metro |
0.3 |
3.021 |
0.00583 |
1.885 |
| Metro |
0.5 |
3.482 |
0.00224 |
3.565 |
| Metro |
0.9 |
4.878 |
9.29e-05 |
7.367 |
| Metro |
0.99 |
7.079 |
9.59e-07 |
35.204 |
| DEMetro_Z |
0.0 |
3.077 |
0.00502 |
1.844 |
| DEMetro_Z |
0.3 |
4.520 |
7.2e-05 |
1.773 |
| DEMetro_Z |
0.5 |
3.676 |
0.00124 |
2.606 |
| DEMetro_Z |
0.9 |
2.541 |
0.0174 |
1.435 |
| DEMetro_Z |
0.99 |
1.887 |
0.0719 |
1.360 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-3.094
|
0.00597
|
-0.692
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.588
|
0.00196
|
-0.802
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.536
|
0.0201
|
-0.567
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.584
|
0.13
|
-0.354
|
| HMC_vs_DEMetro_Z |
0.99
|
0.127
|
0.9
|
0.028
|
| Metro_vs_SMC |
0.0
|
3.491
|
0.00244
|
0.781
|
| Metro_vs_SMC |
0.3
|
3.046
|
0.00664
|
0.681
|
| Metro_vs_SMC |
0.5
|
3.211
|
0.0046
|
0.718
|
| Metro_vs_SMC |
0.9
|
4.930
|
9.29e-05
|
1.102
|
| Metro_vs_SMC |
0.99
|
7.252
|
6.98e-07
|
1.622
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.505
|
0.149
|
-0.336
|
| Metro_vs_DEMetro_Z |
0.3
|
0.183
|
0.857
|
0.041
|
| Metro_vs_DEMetro_Z |
0.5
|
0.706
|
0.489
|
0.158
|
| Metro_vs_DEMetro_Z |
0.9
|
3.436
|
0.00277
|
0.768
|
| Metro_vs_DEMetro_Z |
0.99
|
6.436
|
3.6e-06
|
1.439
|
| HMC_vs_Metro |
0.0
|
-1.847
|
0.0804
|
-0.413
|
| HMC_vs_Metro |
0.3
|
-2.530
|
0.0204
|
-0.566
|
| HMC_vs_Metro |
0.5
|
-2.533
|
0.0203
|
-0.566
|
| HMC_vs_Metro |
0.9
|
-4.547
|
0.00022
|
-1.017
|
| HMC_vs_Metro |
0.99
|
-7.048
|
1.04e-06
|
-1.576
|
| HMC_vs_SMC |
0.0
|
1.458
|
0.161
|
0.326
|
| HMC_vs_SMC |
0.3
|
1.523
|
0.144
|
0.340
|
| HMC_vs_SMC |
0.5
|
1.379
|
0.184
|
0.308
|
| HMC_vs_SMC |
0.9
|
2.272
|
0.0349
|
0.508
|
| HMC_vs_SMC |
0.99
|
4.575
|
0.000207
|
1.023
|
| DEMetro_Z_vs_SMC |
0.0
|
3.351
|
0.00335
|
0.749
|
| DEMetro_Z_vs_SMC |
0.3
|
4.628
|
0.000184
|
1.035
|
| DEMetro_Z_vs_SMC |
0.5
|
3.633
|
0.00177
|
0.812
|
| DEMetro_Z_vs_SMC |
0.9
|
2.817
|
0.011
|
0.630
|
| DEMetro_Z_vs_SMC |
0.99
|
3.054
|
0.00653
|
0.683
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.023 |
0.022 |
0.010 |
0.106 |
| HMC |
0.3 |
0.022 |
0.017 |
0.011 |
0.407 |
| HMC |
0.5 |
0.024 |
0.019 |
0.008 |
0.639 |
| HMC |
0.9 |
0.026 |
0.020 |
0.012 |
0.534 |
| HMC |
0.99 |
0.036 |
0.018 |
0.012 |
1.464 |
| SMC |
0.0 |
0.020 |
0.022 |
0.010 |
-0.263 |
| SMC |
0.3 |
0.017 |
0.017 |
0.011 |
-0.004 |
| SMC |
0.5 |
0.019 |
0.019 |
0.008 |
0.095 |
| SMC |
0.9 |
0.015 |
0.020 |
0.012 |
-0.376 |
| SMC |
0.99 |
0.008 |
0.018 |
0.012 |
-0.857 |
| Metro |
0.0 |
0.030 |
0.022 |
0.010 |
0.843 |
| Metro |
0.3 |
0.038 |
0.017 |
0.011 |
1.885 |
| Metro |
0.5 |
0.047 |
0.019 |
0.008 |
3.565 |
| Metro |
0.9 |
0.106 |
0.020 |
0.012 |
7.367 |
| Metro |
0.99 |
0.437 |
0.018 |
0.012 |
35.204 |
| DEMetro_Z |
0.0 |
0.040 |
0.022 |
0.010 |
1.844 |
| DEMetro_Z |
0.3 |
0.037 |
0.017 |
0.011 |
1.773 |
| DEMetro_Z |
0.5 |
0.039 |
0.019 |
0.008 |
2.606 |
| DEMetro_Z |
0.9 |
0.037 |
0.020 |
0.012 |
1.435 |
| DEMetro_Z |
0.99 |
0.035 |
0.018 |
0.012 |
1.360 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.106 |
0.916 |
-0.033 |
| HMC |
0.3 |
1.970 |
0.0568 |
0.744 |
| HMC |
0.5 |
0.511 |
0.612 |
0.185 |
| HMC |
0.9 |
1.548 |
0.133 |
0.775 |
| HMC |
0.99 |
1.937 |
0.0621 |
0.859 |
| SMC |
0.0 |
-0.846 |
0.403 |
-0.241 |
| SMC |
0.3 |
-0.190 |
0.851 |
-0.062 |
| SMC |
0.5 |
0.486 |
0.63 |
0.173 |
| SMC |
0.9 |
0.922 |
0.363 |
0.316 |
| SMC |
0.99 |
0.658 |
0.515 |
0.263 |
| Metro |
0.0 |
3.471 |
0.00132 |
1.165 |
| Metro |
0.3 |
3.667 |
0.000803 |
1.366 |
| Metro |
0.5 |
3.534 |
0.00133 |
1.576 |
| Metro |
0.9 |
4.589 |
0.00015 |
4.094 |
| Metro |
0.99 |
4.506 |
0.000236 |
13.144 |
| DEMetro_Z |
0.0 |
3.526 |
0.00147 |
1.748 |
| DEMetro_Z |
0.3 |
4.635 |
6.45e-05 |
2.095 |
| DEMetro_Z |
0.5 |
4.484 |
0.000117 |
2.282 |
| DEMetro_Z |
0.9 |
2.819 |
0.00957 |
1.887 |
| DEMetro_Z |
0.99 |
2.164 |
0.0375 |
0.827 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
0.666
|
0.513
|
0.149
|
| HMC_vs_SMC |
0.3
|
2.261
|
0.0357
|
0.506
|
| HMC_vs_SMC |
0.5
|
0.064
|
0.95
|
0.014
|
| HMC_vs_SMC |
0.9
|
0.955
|
0.352
|
0.213
|
| HMC_vs_SMC |
0.99
|
1.034
|
0.314
|
0.231
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.136
|
0.27
|
-0.254
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.526
|
0.144
|
-0.341
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.337
|
0.197
|
-0.299
|
| Metro_vs_DEMetro_Z |
0.9
|
2.200
|
0.0404
|
0.492
|
| Metro_vs_DEMetro_Z |
0.99
|
4.568
|
0.00021
|
1.021
|
| HMC_vs_Metro |
0.0
|
-3.754
|
0.00134
|
-0.839
|
| HMC_vs_Metro |
0.3
|
-1.599
|
0.126
|
-0.357
|
| HMC_vs_Metro |
0.5
|
-2.485
|
0.0224
|
-0.556
|
| HMC_vs_Metro |
0.9
|
-3.185
|
0.00488
|
-0.712
|
| HMC_vs_Metro |
0.99
|
-4.120
|
0.000583
|
-0.921
|
| HMC_vs_DEMetro_Z |
0.0
|
-3.272
|
0.00401
|
-0.732
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.524
|
0.0207
|
-0.564
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.277
|
0.000407
|
-0.956
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.485
|
0.154
|
-0.332
|
| HMC_vs_DEMetro_Z |
0.99
|
0.067
|
0.947
|
0.015
|
| Metro_vs_SMC |
0.0
|
4.315
|
0.000373
|
0.965
|
| Metro_vs_SMC |
0.3
|
4.154
|
0.00054
|
0.929
|
| Metro_vs_SMC |
0.5
|
2.463
|
0.0235
|
0.551
|
| Metro_vs_SMC |
0.9
|
4.027
|
0.000721
|
0.900
|
| Metro_vs_SMC |
0.99
|
4.647
|
0.000176
|
1.039
|
| DEMetro_Z_vs_SMC |
0.0
|
3.980
|
0.000802
|
0.890
|
| DEMetro_Z_vs_SMC |
0.3
|
4.410
|
0.000301
|
0.986
|
| DEMetro_Z_vs_SMC |
0.5
|
4.117
|
0.000587
|
0.921
|
| DEMetro_Z_vs_SMC |
0.9
|
2.117
|
0.0477
|
0.473
|
| DEMetro_Z_vs_SMC |
0.99
|
1.626
|
0.12
|
0.364
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.030 |
0.031 |
0.016 |
-0.033 |
| HMC |
0.3 |
0.036 |
0.026 |
0.014 |
0.744 |
| HMC |
0.5 |
0.028 |
0.026 |
0.012 |
0.185 |
| HMC |
0.9 |
0.045 |
0.033 |
0.015 |
0.775 |
| HMC |
0.99 |
0.042 |
0.026 |
0.018 |
0.859 |
| SMC |
0.0 |
0.027 |
0.031 |
0.016 |
-0.241 |
| SMC |
0.3 |
0.025 |
0.026 |
0.014 |
-0.062 |
| SMC |
0.5 |
0.028 |
0.026 |
0.012 |
0.173 |
| SMC |
0.9 |
0.038 |
0.033 |
0.015 |
0.316 |
| SMC |
0.99 |
0.031 |
0.026 |
0.018 |
0.263 |
| Metro |
0.0 |
0.049 |
0.031 |
0.016 |
1.165 |
| Metro |
0.3 |
0.045 |
0.026 |
0.014 |
1.366 |
| Metro |
0.5 |
0.045 |
0.026 |
0.012 |
1.576 |
| Metro |
0.9 |
0.096 |
0.033 |
0.015 |
4.094 |
| Metro |
0.99 |
0.264 |
0.026 |
0.018 |
13.144 |
| DEMetro_Z |
0.0 |
0.059 |
0.031 |
0.016 |
1.748 |
| DEMetro_Z |
0.3 |
0.056 |
0.026 |
0.014 |
2.095 |
| DEMetro_Z |
0.5 |
0.054 |
0.026 |
0.012 |
2.282 |
| DEMetro_Z |
0.9 |
0.062 |
0.033 |
0.015 |
1.887 |
| DEMetro_Z |
0.99 |
0.041 |
0.026 |
0.018 |
0.827 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.102 |
0.919 |
0.040 |
| HMC |
0.3 |
2.473 |
0.0183 |
0.907 |
| HMC |
0.5 |
1.945 |
0.0599 |
0.736 |
| HMC |
0.9 |
2.462 |
0.019 |
0.948 |
| HMC |
0.99 |
3.593 |
0.00139 |
2.127 |
| SMC |
0.0 |
-1.475 |
0.15 |
-0.599 |
| SMC |
0.3 |
0.567 |
0.574 |
0.183 |
| SMC |
0.5 |
0.993 |
0.327 |
0.302 |
| SMC |
0.9 |
0.402 |
0.69 |
0.138 |
| SMC |
0.99 |
-0.994 |
0.327 |
-0.289 |
| Metro |
0.0 |
3.991 |
0.000437 |
2.019 |
| Metro |
0.3 |
3.928 |
0.000696 |
3.033 |
| Metro |
0.5 |
3.958 |
0.000753 |
4.760 |
| Metro |
0.9 |
6.505 |
2.6e-06 |
10.601 |
| Metro |
0.99 |
8.149 |
1.25e-07 |
50.693 |
| DEMetro_Z |
0.0 |
5.950 |
5.39e-06 |
4.835 |
| DEMetro_Z |
0.3 |
8.706 |
6.23e-10 |
3.676 |
| DEMetro_Z |
0.5 |
6.305 |
1.65e-06 |
4.142 |
| DEMetro_Z |
0.9 |
5.293 |
1.65e-05 |
3.059 |
| DEMetro_Z |
0.99 |
4.672 |
0.000106 |
3.397 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-2.982
|
0.00766
|
-0.667
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.827
|
0.419
|
-0.185
|
| Metro_vs_DEMetro_Z |
0.5
|
0.435
|
0.668
|
0.097
|
| Metro_vs_DEMetro_Z |
0.9
|
3.980
|
0.000803
|
0.890
|
| Metro_vs_DEMetro_Z |
0.99
|
7.253
|
6.96e-07
|
1.622
|
| DEMetro_Z_vs_SMC |
0.0
|
5.988
|
9.22e-06
|
1.339
|
| DEMetro_Z_vs_SMC |
0.3
|
8.640
|
5.24e-08
|
1.932
|
| DEMetro_Z_vs_SMC |
0.5
|
6.452
|
3.49e-06
|
1.443
|
| DEMetro_Z_vs_SMC |
0.9
|
4.705
|
0.000154
|
1.052
|
| DEMetro_Z_vs_SMC |
0.99
|
4.986
|
8.21e-05
|
1.115
|
| HMC_vs_DEMetro_Z |
0.0
|
-6.084
|
7.51e-06
|
-1.361
|
| HMC_vs_DEMetro_Z |
0.3
|
-6.175
|
6.2e-06
|
-1.381
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.815
|
0.00012
|
-1.077
|
| HMC_vs_DEMetro_Z |
0.9
|
-3.361
|
0.00328
|
-0.752
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.377
|
0.184
|
-0.308
|
| HMC_vs_Metro |
0.0
|
-3.979
|
0.000804
|
-0.890
|
| HMC_vs_Metro |
0.3
|
-3.137
|
0.00542
|
-0.702
|
| HMC_vs_Metro |
0.5
|
-3.298
|
0.00379
|
-0.737
|
| HMC_vs_Metro |
0.9
|
-6.118
|
6.99e-06
|
-1.368
|
| HMC_vs_Metro |
0.99
|
-8.052
|
1.52e-07
|
-1.801
|
| HMC_vs_SMC |
0.0
|
1.514
|
0.147
|
0.339
|
| HMC_vs_SMC |
0.3
|
2.116
|
0.0478
|
0.473
|
| HMC_vs_SMC |
0.5
|
1.493
|
0.152
|
0.334
|
| HMC_vs_SMC |
0.9
|
1.977
|
0.0628
|
0.442
|
| HMC_vs_SMC |
0.99
|
4.176
|
0.000513
|
0.934
|
| Metro_vs_SMC |
0.0
|
5.071
|
6.78e-05
|
1.134
|
| Metro_vs_SMC |
0.3
|
3.613
|
0.00185
|
0.808
|
| Metro_vs_SMC |
0.5
|
3.716
|
0.00147
|
0.831
|
| Metro_vs_SMC |
0.9
|
6.158
|
6.42e-06
|
1.377
|
| Metro_vs_SMC |
0.99
|
8.251
|
1.06e-07
|
1.845
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.031 |
0.030 |
0.005 |
0.040 |
| HMC |
0.3 |
0.033 |
0.027 |
0.007 |
0.907 |
| HMC |
0.5 |
0.032 |
0.028 |
0.006 |
0.736 |
| HMC |
0.9 |
0.035 |
0.028 |
0.008 |
0.948 |
| HMC |
0.99 |
0.042 |
0.025 |
0.008 |
2.127 |
| SMC |
0.0 |
0.028 |
0.030 |
0.005 |
-0.599 |
| SMC |
0.3 |
0.028 |
0.027 |
0.007 |
0.183 |
| SMC |
0.5 |
0.029 |
0.028 |
0.006 |
0.302 |
| SMC |
0.9 |
0.029 |
0.028 |
0.008 |
0.138 |
| SMC |
0.99 |
0.023 |
0.025 |
0.008 |
-0.289 |
| Metro |
0.0 |
0.040 |
0.030 |
0.005 |
2.019 |
| Metro |
0.3 |
0.047 |
0.027 |
0.007 |
3.033 |
| Metro |
0.5 |
0.054 |
0.028 |
0.006 |
4.760 |
| Metro |
0.9 |
0.108 |
0.028 |
0.008 |
10.601 |
| Metro |
0.99 |
0.415 |
0.025 |
0.008 |
50.693 |
| DEMetro_Z |
0.0 |
0.054 |
0.030 |
0.005 |
4.835 |
| DEMetro_Z |
0.3 |
0.051 |
0.027 |
0.007 |
3.676 |
| DEMetro_Z |
0.5 |
0.051 |
0.028 |
0.006 |
4.142 |
| DEMetro_Z |
0.9 |
0.051 |
0.028 |
0.008 |
3.059 |
| DEMetro_Z |
0.99 |
0.051 |
0.025 |
0.008 |
3.397 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.354 |
0.725 |
0.129 |
| HMC |
0.3 |
2.351 |
0.0243 |
0.838 |
| HMC |
0.5 |
1.779 |
0.0839 |
0.664 |
| HMC |
0.9 |
2.189 |
0.0349 |
0.683 |
| HMC |
0.99 |
3.344 |
0.00233 |
1.641 |
| SMC |
0.0 |
-1.439 |
0.159 |
-0.506 |
| SMC |
0.3 |
0.559 |
0.58 |
0.189 |
| SMC |
0.5 |
1.484 |
0.146 |
0.467 |
| SMC |
0.9 |
0.884 |
0.382 |
0.282 |
| SMC |
0.99 |
-1.089 |
0.283 |
-0.344 |
| Metro |
0.0 |
2.744 |
0.00988 |
1.162 |
| Metro |
0.3 |
3.391 |
0.00246 |
2.310 |
| Metro |
0.5 |
4.311 |
0.000277 |
3.441 |
| Metro |
0.9 |
6.521 |
2.09e-06 |
7.548 |
| Metro |
0.99 |
8.419 |
7.54e-08 |
41.070 |
| DEMetro_Z |
0.0 |
4.974 |
4.54e-05 |
3.295 |
| DEMetro_Z |
0.3 |
6.851 |
8.65e-08 |
2.817 |
| DEMetro_Z |
0.5 |
4.661 |
9.56e-05 |
2.955 |
| DEMetro_Z |
0.9 |
3.871 |
0.000656 |
2.169 |
| DEMetro_Z |
0.99 |
3.820 |
0.000872 |
2.716 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
5.133
|
5.92e-05
|
1.148
|
| DEMetro_Z_vs_SMC |
0.3
|
6.475
|
3.32e-06
|
1.448
|
| DEMetro_Z_vs_SMC |
0.5
|
4.469
|
0.000263
|
0.999
|
| DEMetro_Z_vs_SMC |
0.9
|
3.527
|
0.00225
|
0.789
|
| DEMetro_Z_vs_SMC |
0.99
|
4.214
|
0.00047
|
0.942
|
| HMC_vs_Metro |
0.0
|
-2.413
|
0.0261
|
-0.540
|
| HMC_vs_Metro |
0.3
|
-2.739
|
0.013
|
-0.612
|
| HMC_vs_Metro |
0.5
|
-3.240
|
0.00431
|
-0.724
|
| HMC_vs_Metro |
0.9
|
-6.371
|
4.12e-06
|
-1.425
|
| HMC_vs_Metro |
0.99
|
-8.307
|
9.54e-08
|
-1.857
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.807
|
0.0113
|
-0.628
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.717
|
0.482
|
-0.160
|
| Metro_vs_DEMetro_Z |
0.5
|
0.444
|
0.662
|
0.099
|
| Metro_vs_DEMetro_Z |
0.9
|
3.832
|
0.00112
|
0.857
|
| Metro_vs_DEMetro_Z |
0.99
|
7.515
|
4.19e-07
|
1.680
|
| HMC_vs_SMC |
0.0
|
1.730
|
0.0999
|
0.387
|
| HMC_vs_SMC |
0.3
|
1.970
|
0.0636
|
0.440
|
| HMC_vs_SMC |
0.5
|
0.742
|
0.467
|
0.166
|
| HMC_vs_SMC |
0.9
|
1.376
|
0.185
|
0.308
|
| HMC_vs_SMC |
0.99
|
3.639
|
0.00175
|
0.814
|
| Metro_vs_SMC |
0.0
|
3.852
|
0.00108
|
0.861
|
| Metro_vs_SMC |
0.3
|
3.065
|
0.00637
|
0.685
|
| Metro_vs_SMC |
0.5
|
3.569
|
0.00205
|
0.798
|
| Metro_vs_SMC |
0.9
|
6.211
|
5.76e-06
|
1.389
|
| Metro_vs_SMC |
0.99
|
8.543
|
6.23e-08
|
1.910
|
| HMC_vs_DEMetro_Z |
0.0
|
-4.658
|
0.000171
|
-1.042
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.705
|
0.000154
|
-1.052
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.626
|
0.0018
|
-0.811
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.706
|
0.014
|
-0.605
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.312
|
0.205
|
-0.293
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.015 |
0.015 |
0.004 |
0.129 |
| HMC |
0.3 |
0.017 |
0.013 |
0.005 |
0.838 |
| HMC |
0.5 |
0.016 |
0.014 |
0.004 |
0.664 |
| HMC |
0.9 |
0.019 |
0.015 |
0.006 |
0.683 |
| HMC |
0.99 |
0.023 |
0.014 |
0.005 |
1.641 |
| SMC |
0.0 |
0.013 |
0.015 |
0.004 |
-0.506 |
| SMC |
0.3 |
0.014 |
0.013 |
0.005 |
0.189 |
| SMC |
0.5 |
0.015 |
0.014 |
0.004 |
0.467 |
| SMC |
0.9 |
0.017 |
0.015 |
0.006 |
0.282 |
| SMC |
0.99 |
0.013 |
0.014 |
0.005 |
-0.344 |
| Metro |
0.0 |
0.019 |
0.015 |
0.004 |
1.162 |
| Metro |
0.3 |
0.024 |
0.013 |
0.005 |
2.310 |
| Metro |
0.5 |
0.028 |
0.014 |
0.004 |
3.441 |
| Metro |
0.9 |
0.060 |
0.015 |
0.006 |
7.548 |
| Metro |
0.99 |
0.228 |
0.014 |
0.005 |
41.070 |
| DEMetro_Z |
0.0 |
0.027 |
0.015 |
0.004 |
3.295 |
| DEMetro_Z |
0.3 |
0.026 |
0.013 |
0.005 |
2.817 |
| DEMetro_Z |
0.5 |
0.026 |
0.014 |
0.004 |
2.955 |
| DEMetro_Z |
0.9 |
0.028 |
0.015 |
0.006 |
2.169 |
| DEMetro_Z |
0.99 |
0.028 |
0.014 |
0.005 |
2.716 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_high_Dimension
(MvNormal,
correlation,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-4.882 |
3.26e-05 |
-1.253 |
| HMC |
0.3 |
2.023 |
0.0556 |
1.774 |
| HMC |
0.5 |
2.116 |
0.0428 |
0.961 |
| HMC |
0.9 |
6.107 |
5.88e-06 |
9.088 |
| HMC |
0.99 |
4.030 |
0.000648 |
5.235 |
| SMC |
0.0 |
0.425 |
0.673 |
0.171 |
| SMC |
0.3 |
1.908 |
0.0658 |
0.842 |
| SMC |
0.5 |
-0.725 |
0.473 |
-0.200 |
| SMC |
0.9 |
-0.657 |
0.515 |
-0.231 |
| SMC |
0.99 |
0.244 |
0.809 |
0.071 |
| Metro |
0.0 |
14.400 |
5.39e-16 |
5.650 |
| Metro |
0.3 |
4.654 |
0.000169 |
15.657 |
| Metro |
0.5 |
5.218 |
4.63e-05 |
12.304 |
| Metro |
0.9 |
5.626 |
1.98e-05 |
32.631 |
| Metro |
0.99 |
4.250 |
0.000432 |
40.269 |
| DEMetro_Z |
0.0 |
29.309 |
2.79e-17 |
2283.554 |
| DEMetro_Z |
0.3 |
39.444 |
1.08e-19 |
2298.573 |
| DEMetro_Z |
0.5 |
38.616 |
1.6e-19 |
934.866 |
| DEMetro_Z |
0.9 |
43.423 |
1.75e-20 |
668.764 |
| DEMetro_Z |
0.99 |
29.121 |
3.09e-17 |
341.717 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-29.327
|
2.76e-17
|
-6.558
|
| HMC_vs_DEMetro_Z |
0.3
|
-39.454
|
1.08e-19
|
-8.822
|
| HMC_vs_DEMetro_Z |
0.5
|
-38.852
|
1.44e-19
|
-8.687
|
| HMC_vs_DEMetro_Z |
0.9
|
-42.736
|
2.39e-20
|
-9.556
|
| HMC_vs_DEMetro_Z |
0.99
|
-29.713
|
2.16e-17
|
-6.644
|
| Metro_vs_SMC |
0.0
|
12.856
|
8.02e-11
|
2.875
|
| Metro_vs_SMC |
0.3
|
4.506
|
0.000242
|
1.008
|
| Metro_vs_SMC |
0.5
|
5.213
|
4.96e-05
|
1.166
|
| Metro_vs_SMC |
0.9
|
5.627
|
2e-05
|
1.258
|
| Metro_vs_SMC |
0.99
|
4.242
|
0.000441
|
0.948
|
| Metro_vs_DEMetro_Z |
0.0
|
-29.237
|
2.92e-17
|
-6.538
|
| Metro_vs_DEMetro_Z |
0.3
|
-38.898
|
1.4e-19
|
-8.698
|
| Metro_vs_DEMetro_Z |
0.5
|
-37.882
|
2.31e-19
|
-8.471
|
| Metro_vs_DEMetro_Z |
0.9
|
-33.063
|
2.95e-18
|
-7.393
|
| Metro_vs_DEMetro_Z |
0.99
|
-17.384
|
4e-13
|
-3.887
|
| HMC_vs_Metro |
0.0
|
-19.482
|
5.13e-14
|
-4.356
|
| HMC_vs_Metro |
0.3
|
-4.276
|
0.000408
|
-0.956
|
| HMC_vs_Metro |
0.5
|
-4.614
|
0.000189
|
-1.032
|
| HMC_vs_Metro |
0.9
|
-3.634
|
0.00177
|
-0.813
|
| HMC_vs_Metro |
0.99
|
-3.562
|
0.00208
|
-0.796
|
| HMC_vs_SMC |
0.0
|
-4.331
|
0.00036
|
-0.968
|
| HMC_vs_SMC |
0.3
|
1.230
|
0.234
|
0.275
|
| HMC_vs_SMC |
0.5
|
2.972
|
0.00784
|
0.664
|
| HMC_vs_SMC |
0.9
|
6.528
|
2.98e-06
|
1.460
|
| HMC_vs_SMC |
0.99
|
3.825
|
0.00114
|
0.855
|
| DEMetro_Z_vs_SMC |
0.0
|
29.289
|
2.83e-17
|
6.549
|
| DEMetro_Z_vs_SMC |
0.3
|
39.507
|
1.05e-19
|
8.834
|
| DEMetro_Z_vs_SMC |
0.5
|
38.726
|
1.53e-19
|
8.659
|
| DEMetro_Z_vs_SMC |
0.9
|
43.532
|
1.69e-20
|
9.734
|
| DEMetro_Z_vs_SMC |
0.99
|
28.956
|
3.5e-17
|
6.475
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.019 |
0.023 |
0.003 |
-1.253 |
| HMC |
0.3 |
0.026 |
0.021 |
0.003 |
1.774 |
| HMC |
0.5 |
0.029 |
0.022 |
0.008 |
0.961 |
| HMC |
0.9 |
0.110 |
0.020 |
0.010 |
9.088 |
| HMC |
0.99 |
0.110 |
0.020 |
0.017 |
5.235 |
| SMC |
0.0 |
0.023 |
0.023 |
0.003 |
0.171 |
| SMC |
0.3 |
0.024 |
0.021 |
0.003 |
0.842 |
| SMC |
0.5 |
0.020 |
0.022 |
0.008 |
-0.200 |
| SMC |
0.9 |
0.018 |
0.020 |
0.010 |
-0.231 |
| SMC |
0.99 |
0.022 |
0.020 |
0.017 |
0.071 |
| Metro |
0.0 |
0.039 |
0.023 |
0.003 |
5.650 |
| Metro |
0.3 |
0.068 |
0.021 |
0.003 |
15.657 |
| Metro |
0.5 |
0.115 |
0.022 |
0.008 |
12.304 |
| Metro |
0.9 |
0.343 |
0.020 |
0.010 |
32.631 |
| Metro |
0.99 |
0.713 |
0.020 |
0.017 |
40.269 |
| DEMetro_Z |
0.0 |
6.514 |
0.023 |
0.003 |
2283.554 |
| DEMetro_Z |
0.3 |
6.831 |
0.021 |
0.003 |
2298.573 |
| DEMetro_Z |
0.5 |
7.144 |
0.022 |
0.008 |
934.866 |
| DEMetro_Z |
0.9 |
6.644 |
0.020 |
0.010 |
668.764 |
| DEMetro_Z |
0.99 |
5.901 |
0.020 |
0.017 |
341.717 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
7.544 |
1.03e-08 |
3.005 |
| HMC |
0.3 |
1.676 |
0.103 |
0.640 |
| HMC |
0.5 |
3.019 |
0.00541 |
1.532 |
| HMC |
0.9 |
4.214 |
0.000436 |
6.767 |
| HMC |
0.99 |
3.099 |
0.00581 |
7.364 |
| SMC |
0.0 |
2.857 |
0.0069 |
0.877 |
| SMC |
0.3 |
1.048 |
0.303 |
0.452 |
| SMC |
0.5 |
0.792 |
0.433 |
0.269 |
| SMC |
0.9 |
0.851 |
0.4 |
0.279 |
| SMC |
0.99 |
-0.399 |
0.693 |
-0.112 |
| Metro |
0.0 |
10.105 |
3.59e-11 |
4.595 |
| Metro |
0.3 |
7.305 |
2.81e-07 |
6.335 |
| Metro |
0.5 |
5.187 |
4.44e-05 |
7.040 |
| Metro |
0.9 |
8.120 |
1.23e-07 |
23.458 |
| Metro |
0.99 |
4.439 |
0.000282 |
140.313 |
| DEMetro_Z |
0.0 |
25.975 |
2.63e-16 |
40537.036 |
| DEMetro_Z |
0.3 |
34.801 |
1.13e-18 |
44793.345 |
| DEMetro_Z |
0.5 |
29.068 |
3.26e-17 |
22986.462 |
| DEMetro_Z |
0.9 |
37.102 |
3.41e-19 |
13666.123 |
| DEMetro_Z |
0.99 |
35.347 |
8.45e-19 |
10192.793 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
6.814
|
1.67e-06
|
1.524
|
| HMC_vs_SMC |
0.3
|
0.407
|
0.689
|
0.091
|
| HMC_vs_SMC |
0.5
|
2.336
|
0.0306
|
0.522
|
| HMC_vs_SMC |
0.9
|
4.061
|
0.000666
|
0.908
|
| HMC_vs_SMC |
0.99
|
3.113
|
0.00572
|
0.696
|
| Metro_vs_DEMetro_Z |
0.0
|
-25.974
|
2.63e-16
|
-5.808
|
| Metro_vs_DEMetro_Z |
0.3
|
-34.781
|
1.14e-18
|
-7.777
|
| Metro_vs_DEMetro_Z |
0.5
|
-29.050
|
3.29e-17
|
-6.496
|
| Metro_vs_DEMetro_Z |
0.9
|
-36.994
|
3.6e-19
|
-8.272
|
| Metro_vs_DEMetro_Z |
0.99
|
-33.533
|
2.27e-18
|
-7.498
|
| HMC_vs_Metro |
0.0
|
-2.630
|
0.0165
|
-0.588
|
| HMC_vs_Metro |
0.3
|
-6.165
|
6.34e-06
|
-1.378
|
| HMC_vs_Metro |
0.5
|
-3.887
|
0.000993
|
-0.869
|
| HMC_vs_Metro |
0.9
|
-4.982
|
8.27e-05
|
-1.114
|
| HMC_vs_Metro |
0.99
|
-4.389
|
0.000315
|
-0.981
|
| HMC_vs_DEMetro_Z |
0.0
|
-25.973
|
2.63e-16
|
-5.808
|
| HMC_vs_DEMetro_Z |
0.3
|
-34.802
|
1.13e-18
|
-7.782
|
| HMC_vs_DEMetro_Z |
0.5
|
-29.067
|
3.26e-17
|
-6.499
|
| HMC_vs_DEMetro_Z |
0.9
|
-37.029
|
3.54e-19
|
-8.280
|
| HMC_vs_DEMetro_Z |
0.99
|
-35.203
|
9.13e-19
|
-7.872
|
| Metro_vs_SMC |
0.0
|
9.132
|
2.22e-08
|
2.042
|
| Metro_vs_SMC |
0.3
|
6.400
|
3.88e-06
|
1.431
|
| Metro_vs_SMC |
0.5
|
4.758
|
0.000137
|
1.064
|
| Metro_vs_SMC |
0.9
|
7.889
|
2.06e-07
|
1.764
|
| Metro_vs_SMC |
0.99
|
4.432
|
0.000286
|
0.991
|
| DEMetro_Z_vs_SMC |
0.0
|
25.975
|
2.63e-16
|
5.808
|
| DEMetro_Z_vs_SMC |
0.3
|
34.802
|
1.13e-18
|
7.782
|
| DEMetro_Z_vs_SMC |
0.5
|
29.067
|
3.26e-17
|
6.499
|
| DEMetro_Z_vs_SMC |
0.9
|
37.095
|
3.42e-19
|
8.295
|
| DEMetro_Z_vs_SMC |
0.99
|
35.354
|
8.42e-19
|
7.905
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.044 |
0.032 |
0.004 |
3.005 |
| HMC |
0.3 |
0.035 |
0.032 |
0.004 |
0.640 |
| HMC |
0.5 |
0.043 |
0.031 |
0.008 |
1.532 |
| HMC |
0.9 |
0.108 |
0.024 |
0.012 |
6.767 |
| HMC |
0.99 |
0.133 |
0.026 |
0.015 |
7.364 |
| SMC |
0.0 |
0.035 |
0.032 |
0.004 |
0.877 |
| SMC |
0.3 |
0.034 |
0.032 |
0.004 |
0.452 |
| SMC |
0.5 |
0.033 |
0.031 |
0.008 |
0.269 |
| SMC |
0.9 |
0.028 |
0.024 |
0.012 |
0.279 |
| SMC |
0.99 |
0.024 |
0.026 |
0.015 |
-0.112 |
| Metro |
0.0 |
0.050 |
0.032 |
0.004 |
4.595 |
| Metro |
0.3 |
0.059 |
0.032 |
0.004 |
6.335 |
| Metro |
0.5 |
0.087 |
0.031 |
0.008 |
7.040 |
| Metro |
0.9 |
0.315 |
0.024 |
0.012 |
23.458 |
| Metro |
0.99 |
2.081 |
0.026 |
0.015 |
140.313 |
| DEMetro_Z |
0.0 |
162.043 |
0.032 |
0.004 |
40537.036 |
| DEMetro_Z |
0.3 |
185.874 |
0.032 |
0.004 |
44793.345 |
| DEMetro_Z |
0.5 |
180.854 |
0.031 |
0.008 |
22986.462 |
| DEMetro_Z |
0.9 |
169.617 |
0.024 |
0.012 |
13666.123 |
| DEMetro_Z |
0.99 |
149.359 |
0.026 |
0.015 |
10192.793 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.370 |
0.714 |
-0.095 |
| HMC |
0.3 |
2.799 |
0.0107 |
2.585 |
| HMC |
0.5 |
3.150 |
0.00379 |
1.518 |
| HMC |
0.9 |
7.009 |
9.81e-07 |
14.088 |
| HMC |
0.99 |
7.436 |
3.3e-07 |
9.426 |
| SMC |
0.0 |
1.284 |
0.208 |
0.525 |
| SMC |
0.3 |
2.273 |
0.0305 |
1.072 |
| SMC |
0.5 |
-0.495 |
0.624 |
-0.126 |
| SMC |
0.9 |
-0.525 |
0.603 |
-0.194 |
| SMC |
0.99 |
-0.348 |
0.73 |
-0.101 |
| Metro |
0.0 |
16.265 |
6.17e-17 |
6.912 |
| Metro |
0.3 |
5.186 |
5.16e-05 |
21.500 |
| Metro |
0.5 |
5.627 |
1.91e-05 |
16.468 |
| Metro |
0.9 |
7.244 |
7.01e-07 |
51.614 |
| Metro |
0.99 |
7.082 |
9.71e-07 |
80.330 |
| DEMetro_Z |
0.0 |
47.774 |
2.94e-21 |
5926.234 |
| DEMetro_Z |
0.3 |
75.569 |
5.05e-25 |
6357.251 |
| DEMetro_Z |
0.5 |
69.400 |
2.52e-24 |
2342.786 |
| DEMetro_Z |
0.9 |
80.444 |
1.53e-25 |
1850.420 |
| DEMetro_Z |
0.99 |
61.495 |
2.45e-23 |
890.174 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-47.734
|
2.98e-21
|
-10.674
|
| Metro_vs_DEMetro_Z |
0.3
|
-76.600
|
3.91e-25
|
-17.128
|
| Metro_vs_DEMetro_Z |
0.5
|
-68.487
|
3.26e-24
|
-15.314
|
| Metro_vs_DEMetro_Z |
0.9
|
-73.092
|
9.49e-25
|
-16.344
|
| Metro_vs_DEMetro_Z |
0.99
|
-40.767
|
5.81e-20
|
-9.116
|
| DEMetro_Z_vs_SMC |
0.0
|
47.744
|
2.97e-21
|
10.676
|
| DEMetro_Z_vs_SMC |
0.3
|
75.681
|
4.91e-25
|
16.923
|
| DEMetro_Z_vs_SMC |
0.5
|
69.462
|
2.49e-24
|
15.532
|
| DEMetro_Z_vs_SMC |
0.9
|
79.890
|
1.76e-25
|
17.864
|
| DEMetro_Z_vs_SMC |
0.99
|
61.124
|
2.8e-23
|
13.668
|
| HMC_vs_DEMetro_Z |
0.0
|
-47.767
|
2.94e-21
|
-10.681
|
| HMC_vs_DEMetro_Z |
0.3
|
-75.788
|
4.78e-25
|
-16.947
|
| HMC_vs_DEMetro_Z |
0.5
|
-69.673
|
2.35e-24
|
-15.579
|
| HMC_vs_DEMetro_Z |
0.9
|
-76.212
|
4.3e-25
|
-17.041
|
| HMC_vs_DEMetro_Z |
0.99
|
-62.215
|
2e-23
|
-13.912
|
| HMC_vs_Metro |
0.0
|
-16.557
|
9.57e-13
|
-3.702
|
| HMC_vs_Metro |
0.3
|
-4.675
|
0.000165
|
-1.045
|
| HMC_vs_Metro |
0.5
|
-4.927
|
9.36e-05
|
-1.102
|
| HMC_vs_Metro |
0.9
|
-4.869
|
0.000107
|
-1.089
|
| HMC_vs_Metro |
0.99
|
-6.160
|
6.41e-06
|
-1.377
|
| HMC_vs_SMC |
0.0
|
-1.736
|
0.0988
|
-0.388
|
| HMC_vs_SMC |
0.3
|
1.792
|
0.0892
|
0.401
|
| HMC_vs_SMC |
0.5
|
3.815
|
0.00117
|
0.853
|
| HMC_vs_SMC |
0.9
|
7.412
|
5.11e-07
|
1.657
|
| HMC_vs_SMC |
0.99
|
7.223
|
7.39e-07
|
1.615
|
| Metro_vs_SMC |
0.0
|
15.020
|
5.38e-12
|
3.359
|
| Metro_vs_SMC |
0.3
|
5.029
|
7.45e-05
|
1.124
|
| Metro_vs_SMC |
0.5
|
5.622
|
2.02e-05
|
1.257
|
| Metro_vs_SMC |
0.9
|
7.218
|
7.46e-07
|
1.614
|
| Metro_vs_SMC |
0.99
|
7.098
|
9.45e-07
|
1.587
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.095 |
| HMC |
0.3 |
0.032 |
0.028 |
0.002 |
2.585 |
| HMC |
0.5 |
0.035 |
0.028 |
0.005 |
1.518 |
| HMC |
0.9 |
0.102 |
0.024 |
0.006 |
14.088 |
| HMC |
0.99 |
0.126 |
0.025 |
0.011 |
9.426 |
| SMC |
0.0 |
0.030 |
0.029 |
0.002 |
0.525 |
| SMC |
0.3 |
0.030 |
0.028 |
0.002 |
1.072 |
| SMC |
0.5 |
0.027 |
0.028 |
0.005 |
-0.126 |
| SMC |
0.9 |
0.023 |
0.024 |
0.006 |
-0.194 |
| SMC |
0.99 |
0.024 |
0.025 |
0.011 |
-0.101 |
| Metro |
0.0 |
0.040 |
0.029 |
0.002 |
6.912 |
| Metro |
0.3 |
0.064 |
0.028 |
0.002 |
21.500 |
| Metro |
0.5 |
0.104 |
0.028 |
0.005 |
16.468 |
| Metro |
0.9 |
0.310 |
0.024 |
0.006 |
51.614 |
| Metro |
0.99 |
0.883 |
0.025 |
0.011 |
80.330 |
| DEMetro_Z |
0.0 |
9.865 |
0.029 |
0.002 |
5926.234 |
| DEMetro_Z |
0.3 |
10.790 |
0.028 |
0.002 |
6357.251 |
| DEMetro_Z |
0.5 |
10.797 |
0.028 |
0.005 |
2342.786 |
| DEMetro_Z |
0.9 |
10.273 |
0.024 |
0.006 |
1850.420 |
| DEMetro_Z |
0.99 |
9.530 |
0.025 |
0.011 |
890.174 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-1.217 |
0.233 |
-0.317 |
| HMC |
0.3 |
2.588 |
0.0167 |
2.117 |
| HMC |
0.5 |
3.468 |
0.00177 |
1.813 |
| HMC |
0.9 |
7.354 |
5.12e-07 |
17.398 |
| HMC |
0.99 |
9.186 |
1.04e-08 |
10.525 |
| SMC |
0.0 |
1.124 |
0.27 |
0.477 |
| SMC |
0.3 |
2.021 |
0.0526 |
0.947 |
| SMC |
0.5 |
-0.303 |
0.763 |
-0.083 |
| SMC |
0.9 |
0.012 |
0.991 |
0.005 |
| SMC |
0.99 |
-0.369 |
0.714 |
-0.109 |
| Metro |
0.0 |
15.708 |
5.36e-17 |
6.257 |
| Metro |
0.3 |
5.426 |
3e-05 |
18.167 |
| Metro |
0.5 |
5.743 |
1.49e-05 |
17.632 |
| Metro |
0.9 |
8.135 |
1.29e-07 |
61.772 |
| Metro |
0.99 |
10.706 |
1.69e-09 |
68.489 |
| DEMetro_Z |
0.0 |
64.681 |
8.61e-24 |
403.669 |
| DEMetro_Z |
0.3 |
83.682 |
5.93e-26 |
396.127 |
| DEMetro_Z |
0.5 |
68.315 |
2.15e-24 |
210.010 |
| DEMetro_Z |
0.9 |
63.459 |
8.7e-24 |
192.063 |
| DEMetro_Z |
0.99 |
70.713 |
1.46e-25 |
94.880 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
65.737
|
7.07e-24
|
14.699
|
| DEMetro_Z_vs_SMC |
0.3
|
82.442
|
9.71e-26
|
18.435
|
| DEMetro_Z_vs_SMC |
0.5
|
69.248
|
2.64e-24
|
15.484
|
| DEMetro_Z_vs_SMC |
0.9
|
64.299
|
1.07e-23
|
14.378
|
| DEMetro_Z_vs_SMC |
0.99
|
69.947
|
2.18e-24
|
15.641
|
| HMC_vs_Metro |
0.0
|
-17.508
|
3.52e-13
|
-3.915
|
| HMC_vs_Metro |
0.3
|
-4.944
|
9.01e-05
|
-1.106
|
| HMC_vs_Metro |
0.5
|
-4.959
|
8.71e-05
|
-1.109
|
| HMC_vs_Metro |
0.9
|
-5.662
|
1.85e-05
|
-1.266
|
| HMC_vs_Metro |
0.99
|
-8.919
|
3.22e-08
|
-1.994
|
| Metro_vs_DEMetro_Z |
0.0
|
-63.564
|
1.34e-23
|
-14.213
|
| Metro_vs_DEMetro_Z |
0.3
|
-61.312
|
2.64e-23
|
-13.710
|
| Metro_vs_DEMetro_Z |
0.5
|
-51.297
|
7.67e-22
|
-11.470
|
| Metro_vs_DEMetro_Z |
0.9
|
-13.805
|
2.35e-11
|
-3.087
|
| Metro_vs_DEMetro_Z |
0.99
|
-3.993
|
0.000779
|
-0.893
|
| HMC_vs_SMC |
0.0
|
-2.000
|
0.06
|
-0.447
|
| HMC_vs_SMC |
0.3
|
1.534
|
0.142
|
0.343
|
| HMC_vs_SMC |
0.5
|
3.827
|
0.00114
|
0.856
|
| HMC_vs_SMC |
0.9
|
7.865
|
2.16e-07
|
1.759
|
| HMC_vs_SMC |
0.99
|
9.052
|
2.55e-08
|
2.024
|
| Metro_vs_SMC |
0.0
|
12.585
|
1.15e-10
|
2.814
|
| Metro_vs_SMC |
0.3
|
5.208
|
5.01e-05
|
1.164
|
| Metro_vs_SMC |
0.5
|
5.711
|
1.67e-05
|
1.277
|
| Metro_vs_SMC |
0.9
|
8.080
|
1.45e-07
|
1.807
|
| Metro_vs_SMC |
0.99
|
10.772
|
1.57e-09
|
2.409
|
| HMC_vs_DEMetro_Z |
0.0
|
-64.318
|
1.07e-23
|
-14.382
|
| HMC_vs_DEMetro_Z |
0.3
|
-79.815
|
1.79e-25
|
-17.847
|
| HMC_vs_DEMetro_Z |
0.5
|
-66.095
|
6.38e-24
|
-14.779
|
| HMC_vs_DEMetro_Z |
0.9
|
-45.039
|
8.92e-21
|
-10.071
|
| HMC_vs_DEMetro_Z |
0.99
|
-50.422
|
1.06e-21
|
-11.275
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.014 |
0.014 |
0.001 |
-0.317 |
| HMC |
0.3 |
0.017 |
0.014 |
0.001 |
2.117 |
| HMC |
0.5 |
0.020 |
0.015 |
0.003 |
1.813 |
| HMC |
0.9 |
0.065 |
0.013 |
0.003 |
17.398 |
| HMC |
0.99 |
0.076 |
0.014 |
0.006 |
10.525 |
| SMC |
0.0 |
0.015 |
0.014 |
0.001 |
0.477 |
| SMC |
0.3 |
0.015 |
0.014 |
0.001 |
0.947 |
| SMC |
0.5 |
0.014 |
0.015 |
0.003 |
-0.083 |
| SMC |
0.9 |
0.013 |
0.013 |
0.003 |
0.005 |
| SMC |
0.99 |
0.014 |
0.014 |
0.006 |
-0.109 |
| Metro |
0.0 |
0.023 |
0.014 |
0.001 |
6.257 |
| Metro |
0.3 |
0.039 |
0.014 |
0.001 |
18.167 |
| Metro |
0.5 |
0.063 |
0.015 |
0.003 |
17.632 |
| Metro |
0.9 |
0.197 |
0.013 |
0.003 |
61.772 |
| Metro |
0.99 |
0.419 |
0.014 |
0.006 |
68.489 |
| DEMetro_Z |
0.0 |
0.588 |
0.014 |
0.001 |
403.669 |
| DEMetro_Z |
0.3 |
0.561 |
0.014 |
0.001 |
396.127 |
| DEMetro_Z |
0.5 |
0.587 |
0.015 |
0.003 |
210.010 |
| DEMetro_Z |
0.9 |
0.585 |
0.013 |
0.003 |
192.063 |
| DEMetro_Z |
0.99 |
0.575 |
0.014 |
0.006 |
94.880 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-4.549 |
6.33e-05 |
-1.256 |
| HMC |
0.3 |
2.361 |
0.0261 |
1.351 |
| HMC |
0.5 |
3.019 |
0.0055 |
1.593 |
| HMC |
0.9 |
3.422 |
0.00274 |
5.599 |
| HMC |
0.99 |
3.606 |
0.00178 |
5.525 |
| SMC |
0.0 |
-0.871 |
0.389 |
-0.288 |
| SMC |
0.3 |
0.624 |
0.537 |
0.274 |
| SMC |
0.5 |
0.008 |
0.994 |
0.002 |
| SMC |
0.9 |
-0.961 |
0.343 |
-0.317 |
| SMC |
0.99 |
0.627 |
0.535 |
0.200 |
| Metro |
0.0 |
12.718 |
1.41e-14 |
4.874 |
| Metro |
0.3 |
6.473 |
2.92e-06 |
12.415 |
| Metro |
0.5 |
7.179 |
7.06e-07 |
15.244 |
| Metro |
0.9 |
5.629 |
1.98e-05 |
43.131 |
| Metro |
0.99 |
6.536 |
2.92e-06 |
90.252 |
| DEMetro_Z |
0.0 |
24.191 |
9.77e-16 |
3800.529 |
| DEMetro_Z |
0.3 |
22.861 |
2.77e-15 |
4104.403 |
| DEMetro_Z |
0.5 |
31.626 |
6.76e-18 |
1622.585 |
| DEMetro_Z |
0.9 |
30.516 |
1.31e-17 |
1137.494 |
| DEMetro_Z |
0.99 |
27.888 |
6.99e-17 |
565.433 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-24.197
|
9.73e-16
|
-5.411
|
| HMC_vs_DEMetro_Z |
0.3
|
-22.851
|
2.79e-15
|
-5.110
|
| HMC_vs_DEMetro_Z |
0.5
|
-31.632
|
6.74e-18
|
-7.073
|
| HMC_vs_DEMetro_Z |
0.9
|
-30.393
|
1.42e-17
|
-6.796
|
| HMC_vs_DEMetro_Z |
0.99
|
-28.026
|
6.42e-17
|
-6.267
|
| Metro_vs_SMC |
0.0
|
16.962
|
6.22e-13
|
3.793
|
| Metro_vs_SMC |
0.3
|
6.548
|
2.86e-06
|
1.464
|
| Metro_vs_SMC |
0.5
|
6.914
|
1.36e-06
|
1.546
|
| Metro_vs_SMC |
0.9
|
5.707
|
1.68e-05
|
1.276
|
| Metro_vs_SMC |
0.99
|
6.502
|
3.14e-06
|
1.454
|
| Metro_vs_DEMetro_Z |
0.0
|
-24.170
|
9.93e-16
|
-5.405
|
| Metro_vs_DEMetro_Z |
0.3
|
-22.775
|
2.97e-15
|
-5.093
|
| Metro_vs_DEMetro_Z |
0.5
|
-31.636
|
6.72e-18
|
-7.074
|
| Metro_vs_DEMetro_Z |
0.9
|
-28.688
|
4.16e-17
|
-6.415
|
| Metro_vs_DEMetro_Z |
0.99
|
-17.663
|
3.01e-13
|
-3.950
|
| HMC_vs_Metro |
0.0
|
-19.438
|
5.34e-14
|
-4.347
|
| HMC_vs_Metro |
0.3
|
-5.747
|
1.54e-05
|
-1.285
|
| HMC_vs_Metro |
0.5
|
-5.912
|
1.08e-05
|
-1.322
|
| HMC_vs_Metro |
0.9
|
-5.193
|
5.18e-05
|
-1.161
|
| HMC_vs_Metro |
0.99
|
-5.760
|
1.5e-05
|
-1.288
|
| HMC_vs_SMC |
0.0
|
-3.962
|
0.000836
|
-0.886
|
| HMC_vs_SMC |
0.3
|
1.625
|
0.121
|
0.363
|
| HMC_vs_SMC |
0.5
|
3.382
|
0.00313
|
0.756
|
| HMC_vs_SMC |
0.9
|
3.836
|
0.00111
|
0.858
|
| HMC_vs_SMC |
0.99
|
3.384
|
0.00311
|
0.757
|
| DEMetro_Z_vs_SMC |
0.0
|
24.193
|
9.76e-16
|
5.410
|
| DEMetro_Z_vs_SMC |
0.3
|
22.864
|
2.76e-15
|
5.113
|
| DEMetro_Z_vs_SMC |
0.5
|
31.619
|
6.79e-18
|
7.070
|
| DEMetro_Z_vs_SMC |
0.9
|
30.491
|
1.34e-17
|
6.818
|
| DEMetro_Z_vs_SMC |
0.99
|
28.004
|
6.51e-17
|
6.262
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.019 |
0.023 |
0.003 |
-1.256 |
| HMC |
0.3 |
0.025 |
0.021 |
0.003 |
1.351 |
| HMC |
0.5 |
0.034 |
0.022 |
0.008 |
1.593 |
| HMC |
0.9 |
0.075 |
0.020 |
0.010 |
5.599 |
| HMC |
0.99 |
0.115 |
0.020 |
0.017 |
5.525 |
| SMC |
0.0 |
0.022 |
0.023 |
0.003 |
-0.288 |
| SMC |
0.3 |
0.022 |
0.021 |
0.003 |
0.274 |
| SMC |
0.5 |
0.022 |
0.022 |
0.008 |
0.002 |
| SMC |
0.9 |
0.017 |
0.020 |
0.010 |
-0.317 |
| SMC |
0.99 |
0.024 |
0.020 |
0.017 |
0.200 |
| Metro |
0.0 |
0.037 |
0.023 |
0.003 |
4.874 |
| Metro |
0.3 |
0.058 |
0.021 |
0.003 |
12.415 |
| Metro |
0.5 |
0.138 |
0.022 |
0.008 |
15.244 |
| Metro |
0.9 |
0.447 |
0.020 |
0.010 |
43.131 |
| Metro |
0.99 |
1.574 |
0.020 |
0.017 |
90.252 |
| DEMetro_Z |
0.0 |
10.826 |
0.023 |
0.003 |
3800.529 |
| DEMetro_Z |
0.3 |
12.181 |
0.021 |
0.003 |
4104.403 |
| DEMetro_Z |
0.5 |
12.383 |
0.022 |
0.008 |
1622.585 |
| DEMetro_Z |
0.9 |
11.287 |
0.020 |
0.010 |
1137.494 |
| DEMetro_Z |
0.99 |
9.751 |
0.020 |
0.017 |
565.433 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
7.671 |
6.23e-09 |
2.974 |
| HMC |
0.3 |
3.030 |
0.00479 |
1.259 |
| HMC |
0.5 |
3.424 |
0.00192 |
1.706 |
| HMC |
0.9 |
5.110 |
5.68e-05 |
9.223 |
| HMC |
0.99 |
3.113 |
0.0057 |
12.524 |
| SMC |
0.0 |
-0.261 |
0.795 |
-0.099 |
| SMC |
0.3 |
-0.696 |
0.491 |
-0.204 |
| SMC |
0.5 |
-0.108 |
0.915 |
-0.030 |
| SMC |
0.9 |
1.950 |
0.0588 |
0.679 |
| SMC |
0.99 |
-1.125 |
0.268 |
-0.373 |
| Metro |
0.0 |
11.465 |
1.4e-12 |
5.113 |
| Metro |
0.3 |
8.797 |
1.05e-08 |
6.934 |
| Metro |
0.5 |
6.568 |
1.97e-06 |
8.065 |
| Metro |
0.9 |
7.489 |
4.18e-07 |
25.742 |
| Metro |
0.99 |
24.574 |
4.34e-16 |
53.291 |
| DEMetro_Z |
0.0 |
8.273 |
1.01e-07 |
4989.047 |
| DEMetro_Z |
0.3 |
12.419 |
1.45e-10 |
5354.728 |
| DEMetro_Z |
0.5 |
8.520 |
6.5e-08 |
2386.024 |
| DEMetro_Z |
0.9 |
10.352 |
3e-09 |
1829.836 |
| DEMetro_Z |
0.99 |
14.557 |
9.31e-12 |
1482.951 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
7.865
|
2.16e-07
|
1.759
|
| HMC_vs_SMC |
0.3
|
4.064
|
0.000662
|
0.909
|
| HMC_vs_SMC |
0.5
|
3.731
|
0.00142
|
0.834
|
| HMC_vs_SMC |
0.9
|
4.861
|
0.000109
|
1.087
|
| HMC_vs_SMC |
0.99
|
3.317
|
0.00363
|
0.742
|
| Metro_vs_DEMetro_Z |
0.0
|
-8.265
|
1.03e-07
|
-1.848
|
| Metro_vs_DEMetro_Z |
0.3
|
-12.408
|
1.47e-10
|
-2.774
|
| Metro_vs_DEMetro_Z |
0.5
|
-8.504
|
6.69e-08
|
-1.901
|
| Metro_vs_DEMetro_Z |
0.9
|
-10.186
|
3.91e-09
|
-2.278
|
| Metro_vs_DEMetro_Z |
0.99
|
-14.001
|
1.84e-11
|
-3.131
|
| HMC_vs_Metro |
0.0
|
-5.103
|
6.32e-05
|
-1.141
|
| HMC_vs_Metro |
0.3
|
-7.012
|
1.12e-06
|
-1.568
|
| HMC_vs_Metro |
0.5
|
-5.093
|
6.46e-05
|
-1.139
|
| HMC_vs_Metro |
0.9
|
-3.845
|
0.00109
|
-0.860
|
| HMC_vs_Metro |
0.99
|
-7.762
|
2.61e-07
|
-1.736
|
| HMC_vs_DEMetro_Z |
0.0
|
-8.267
|
1.02e-07
|
-1.849
|
| HMC_vs_DEMetro_Z |
0.3
|
-12.415
|
1.46e-10
|
-2.776
|
| HMC_vs_DEMetro_Z |
0.5
|
-8.512
|
6.59e-08
|
-1.903
|
| HMC_vs_DEMetro_Z |
0.9
|
-10.298
|
3.27e-09
|
-2.303
|
| HMC_vs_DEMetro_Z |
0.99
|
-14.635
|
8.49e-12
|
-3.272
|
| Metro_vs_SMC |
0.0
|
14.026
|
1.78e-11
|
3.136
|
| Metro_vs_SMC |
0.3
|
9.217
|
1.93e-08
|
2.061
|
| Metro_vs_SMC |
0.5
|
6.458
|
3.44e-06
|
1.444
|
| Metro_vs_SMC |
0.9
|
7.393
|
5.3e-07
|
1.653
|
| Metro_vs_SMC |
0.99
|
24.597
|
7.19e-16
|
5.500
|
| DEMetro_Z_vs_SMC |
0.0
|
8.271
|
1.02e-07
|
1.850
|
| DEMetro_Z_vs_SMC |
0.3
|
12.420
|
1.45e-10
|
2.777
|
| DEMetro_Z_vs_SMC |
0.5
|
8.521
|
6.49e-08
|
1.905
|
| DEMetro_Z_vs_SMC |
0.9
|
10.346
|
3.04e-09
|
2.313
|
| DEMetro_Z_vs_SMC |
0.99
|
14.577
|
9.09e-12
|
3.260
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.044 |
0.032 |
0.004 |
2.974 |
| HMC |
0.3 |
0.038 |
0.032 |
0.004 |
1.259 |
| HMC |
0.5 |
0.045 |
0.031 |
0.008 |
1.706 |
| HMC |
0.9 |
0.139 |
0.024 |
0.012 |
9.223 |
| HMC |
0.99 |
0.209 |
0.026 |
0.015 |
12.524 |
| SMC |
0.0 |
0.031 |
0.032 |
0.004 |
-0.099 |
| SMC |
0.3 |
0.031 |
0.032 |
0.004 |
-0.204 |
| SMC |
0.5 |
0.031 |
0.031 |
0.008 |
-0.030 |
| SMC |
0.9 |
0.033 |
0.024 |
0.012 |
0.679 |
| SMC |
0.99 |
0.020 |
0.026 |
0.015 |
-0.373 |
| Metro |
0.0 |
0.052 |
0.032 |
0.004 |
5.113 |
| Metro |
0.3 |
0.061 |
0.032 |
0.004 |
6.934 |
| Metro |
0.5 |
0.095 |
0.031 |
0.008 |
8.065 |
| Metro |
0.9 |
0.344 |
0.024 |
0.012 |
25.742 |
| Metro |
0.99 |
0.806 |
0.026 |
0.015 |
53.291 |
| DEMetro_Z |
0.0 |
19.971 |
0.032 |
0.004 |
4989.047 |
| DEMetro_Z |
0.3 |
22.248 |
0.032 |
0.004 |
5354.728 |
| DEMetro_Z |
0.5 |
18.801 |
0.031 |
0.008 |
2386.024 |
| DEMetro_Z |
0.9 |
22.732 |
0.024 |
0.012 |
1829.836 |
| DEMetro_Z |
0.99 |
21.752 |
0.026 |
0.015 |
1482.951 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.398 |
0.693 |
0.112 |
| HMC |
0.3 |
3.650 |
0.00116 |
2.053 |
| HMC |
0.5 |
4.371 |
0.00016 |
2.241 |
| HMC |
0.9 |
4.633 |
0.000172 |
9.867 |
| HMC |
0.99 |
5.278 |
3.95e-05 |
10.408 |
| SMC |
0.0 |
-0.345 |
0.732 |
-0.109 |
| SMC |
0.3 |
0.505 |
0.617 |
0.222 |
| SMC |
0.5 |
-0.113 |
0.911 |
-0.030 |
| SMC |
0.9 |
0.140 |
0.89 |
0.046 |
| SMC |
0.99 |
0.310 |
0.758 |
0.094 |
| Metro |
0.0 |
15.040 |
9.45e-16 |
6.603 |
| Metro |
0.3 |
7.827 |
2e-07 |
16.965 |
| Metro |
0.5 |
7.831 |
2.05e-07 |
19.262 |
| Metro |
0.9 |
6.073 |
7.66e-06 |
64.349 |
| Metro |
0.99 |
7.722 |
2.82e-07 |
123.279 |
| DEMetro_Z |
0.0 |
26.890 |
1.38e-16 |
5430.913 |
| DEMetro_Z |
0.3 |
25.479 |
3.75e-16 |
5841.761 |
| DEMetro_Z |
0.5 |
30.963 |
1e-17 |
2227.015 |
| DEMetro_Z |
0.9 |
27.656 |
8.21e-17 |
1699.151 |
| DEMetro_Z |
0.99 |
29.131 |
3.12e-17 |
767.285 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-26.858
|
1.41e-16
|
-6.006
|
| Metro_vs_DEMetro_Z |
0.3
|
-25.373
|
4.05e-16
|
-5.674
|
| Metro_vs_DEMetro_Z |
0.5
|
-30.973
|
9.98e-18
|
-6.926
|
| Metro_vs_DEMetro_Z |
0.9
|
-26.442
|
1.89e-16
|
-5.913
|
| Metro_vs_DEMetro_Z |
0.99
|
-18.991
|
8.15e-14
|
-4.246
|
| DEMetro_Z_vs_SMC |
0.0
|
26.891
|
1.38e-16
|
6.013
|
| DEMetro_Z_vs_SMC |
0.3
|
25.488
|
3.73e-16
|
5.699
|
| DEMetro_Z_vs_SMC |
0.5
|
30.957
|
1.01e-17
|
6.922
|
| DEMetro_Z_vs_SMC |
0.9
|
27.636
|
8.33e-17
|
6.180
|
| DEMetro_Z_vs_SMC |
0.99
|
29.221
|
2.95e-17
|
6.534
|
| HMC_vs_DEMetro_Z |
0.0
|
-26.887
|
1.39e-16
|
-6.012
|
| HMC_vs_DEMetro_Z |
0.3
|
-25.468
|
3.78e-16
|
-5.695
|
| HMC_vs_DEMetro_Z |
0.5
|
-30.949
|
1.01e-17
|
-6.920
|
| HMC_vs_DEMetro_Z |
0.9
|
-27.479
|
9.25e-17
|
-6.145
|
| HMC_vs_DEMetro_Z |
0.99
|
-29.297
|
2.81e-17
|
-6.551
|
| HMC_vs_Metro |
0.0
|
-16.645
|
8.71e-13
|
-3.722
|
| HMC_vs_Metro |
0.3
|
-7.169
|
8.21e-07
|
-1.603
|
| HMC_vs_Metro |
0.5
|
-6.537
|
2.92e-06
|
-1.462
|
| HMC_vs_Metro |
0.9
|
-5.426
|
3.1e-05
|
-1.213
|
| HMC_vs_Metro |
0.99
|
-6.758
|
1.86e-06
|
-1.511
|
| HMC_vs_SMC |
0.0
|
0.822
|
0.421
|
0.184
|
| HMC_vs_SMC |
0.3
|
2.534
|
0.0202
|
0.567
|
| HMC_vs_SMC |
0.5
|
5.001
|
7.94e-05
|
1.118
|
| HMC_vs_SMC |
0.9
|
4.803
|
0.000124
|
1.074
|
| HMC_vs_SMC |
0.99
|
5.180
|
5.33e-05
|
1.158
|
| Metro_vs_SMC |
0.0
|
15.875
|
2.02e-12
|
3.550
|
| Metro_vs_SMC |
0.3
|
7.931
|
1.91e-07
|
1.773
|
| Metro_vs_SMC |
0.5
|
7.697
|
2.96e-07
|
1.721
|
| Metro_vs_SMC |
0.9
|
6.109
|
7.12e-06
|
1.366
|
| Metro_vs_SMC |
0.99
|
7.700
|
2.94e-07
|
1.722
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.029 |
0.029 |
0.002 |
0.112 |
| HMC |
0.3 |
0.031 |
0.028 |
0.002 |
2.053 |
| HMC |
0.5 |
0.038 |
0.028 |
0.005 |
2.241 |
| HMC |
0.9 |
0.079 |
0.024 |
0.006 |
9.867 |
| HMC |
0.99 |
0.136 |
0.025 |
0.011 |
10.408 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.109 |
| SMC |
0.3 |
0.028 |
0.028 |
0.002 |
0.222 |
| SMC |
0.5 |
0.028 |
0.028 |
0.005 |
-0.030 |
| SMC |
0.9 |
0.025 |
0.024 |
0.006 |
0.046 |
| SMC |
0.99 |
0.026 |
0.025 |
0.011 |
0.094 |
| Metro |
0.0 |
0.040 |
0.029 |
0.002 |
6.603 |
| Metro |
0.3 |
0.057 |
0.028 |
0.002 |
16.965 |
| Metro |
0.5 |
0.116 |
0.028 |
0.005 |
19.262 |
| Metro |
0.9 |
0.381 |
0.024 |
0.006 |
64.349 |
| Metro |
0.99 |
1.341 |
0.025 |
0.011 |
123.279 |
| DEMetro_Z |
0.0 |
9.043 |
0.029 |
0.002 |
5430.913 |
| DEMetro_Z |
0.3 |
9.917 |
0.028 |
0.002 |
5841.761 |
| DEMetro_Z |
0.5 |
10.265 |
0.028 |
0.005 |
2227.015 |
| DEMetro_Z |
0.9 |
9.435 |
0.024 |
0.006 |
1699.151 |
| DEMetro_Z |
0.99 |
8.218 |
0.025 |
0.011 |
767.285 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-1.574 |
0.125 |
-0.413 |
| HMC |
0.3 |
2.768 |
0.0102 |
1.497 |
| HMC |
0.5 |
4.453 |
0.00014 |
2.444 |
| HMC |
0.9 |
4.871 |
0.000102 |
13.055 |
| HMC |
0.99 |
5.254 |
4.29e-05 |
12.822 |
| SMC |
0.0 |
-0.593 |
0.557 |
-0.202 |
| SMC |
0.3 |
0.600 |
0.553 |
0.259 |
| SMC |
0.5 |
-0.271 |
0.788 |
-0.073 |
| SMC |
0.9 |
1.273 |
0.213 |
0.570 |
| SMC |
0.99 |
-0.030 |
0.976 |
-0.010 |
| Metro |
0.0 |
13.359 |
9.94e-15 |
5.526 |
| Metro |
0.3 |
7.883 |
1.67e-07 |
13.947 |
| Metro |
0.5 |
7.813 |
2.15e-07 |
20.551 |
| Metro |
0.9 |
7.550 |
3.89e-07 |
77.732 |
| Metro |
0.99 |
12.553 |
1.19e-10 |
125.394 |
| DEMetro_Z |
0.0 |
62.903 |
1.56e-23 |
650.738 |
| DEMetro_Z |
0.3 |
50.983 |
8.43e-22 |
668.194 |
| DEMetro_Z |
0.5 |
48.038 |
2.46e-21 |
345.227 |
| DEMetro_Z |
0.9 |
84.149 |
4.77e-26 |
322.554 |
| DEMetro_Z |
0.99 |
85.166 |
1.17e-26 |
152.700 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
62.843
|
1.66e-23
|
14.052
|
| DEMetro_Z_vs_SMC |
0.3
|
51.013
|
8.52e-22
|
11.407
|
| DEMetro_Z_vs_SMC |
0.5
|
47.741
|
2.97e-21
|
10.675
|
| DEMetro_Z_vs_SMC |
0.9
|
83.491
|
7.64e-26
|
18.669
|
| DEMetro_Z_vs_SMC |
0.99
|
85.895
|
4.46e-26
|
19.207
|
| HMC_vs_Metro |
0.0
|
-15.612
|
2.72e-12
|
-3.491
|
| HMC_vs_Metro |
0.3
|
-7.290
|
6.48e-07
|
-1.630
|
| HMC_vs_Metro |
0.5
|
-6.699
|
2.1e-06
|
-1.498
|
| HMC_vs_Metro |
0.9
|
-6.672
|
2.22e-06
|
-1.492
|
| HMC_vs_Metro |
0.99
|
-9.928
|
5.91e-09
|
-2.220
|
| Metro_vs_DEMetro_Z |
0.0
|
-63.007
|
1.58e-23
|
-14.089
|
| Metro_vs_DEMetro_Z |
0.3
|
-52.827
|
4.41e-22
|
-11.812
|
| Metro_vs_DEMetro_Z |
0.5
|
-44.285
|
1.23e-20
|
-9.902
|
| Metro_vs_DEMetro_Z |
0.9
|
-21.873
|
6.22e-15
|
-4.891
|
| Metro_vs_DEMetro_Z |
0.99
|
-2.644
|
0.016
|
-0.591
|
| HMC_vs_SMC |
0.0
|
-0.767
|
0.453
|
-0.171
|
| HMC_vs_SMC |
0.3
|
1.867
|
0.0775
|
0.417
|
| HMC_vs_SMC |
0.5
|
5.222
|
4.86e-05
|
1.168
|
| HMC_vs_SMC |
0.9
|
4.830
|
0.000116
|
1.080
|
| HMC_vs_SMC |
0.99
|
5.219
|
4.88e-05
|
1.167
|
| Metro_vs_SMC |
0.0
|
15.814
|
2.17e-12
|
3.536
|
| Metro_vs_SMC |
0.3
|
7.965
|
1.79e-07
|
1.781
|
| Metro_vs_SMC |
0.5
|
7.693
|
2.98e-07
|
1.720
|
| Metro_vs_SMC |
0.9
|
7.587
|
3.65e-07
|
1.696
|
| Metro_vs_SMC |
0.99
|
12.501
|
1.29e-10
|
2.795
|
| HMC_vs_DEMetro_Z |
0.0
|
-62.887
|
1.64e-23
|
-14.062
|
| HMC_vs_DEMetro_Z |
0.3
|
-51.666
|
6.7e-22
|
-11.553
|
| HMC_vs_DEMetro_Z |
0.5
|
-47.112
|
3.82e-21
|
-10.535
|
| HMC_vs_DEMetro_Z |
0.9
|
-61.016
|
2.89e-23
|
-13.644
|
| HMC_vs_DEMetro_Z |
0.99
|
-48.190
|
2.49e-21
|
-10.776
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.014 |
0.014 |
0.001 |
-0.413 |
| HMC |
0.3 |
0.016 |
0.014 |
0.001 |
1.497 |
| HMC |
0.5 |
0.021 |
0.015 |
0.003 |
2.444 |
| HMC |
0.9 |
0.052 |
0.013 |
0.003 |
13.055 |
| HMC |
0.99 |
0.090 |
0.014 |
0.006 |
12.822 |
| SMC |
0.0 |
0.014 |
0.014 |
0.001 |
-0.202 |
| SMC |
0.3 |
0.014 |
0.014 |
0.001 |
0.259 |
| SMC |
0.5 |
0.015 |
0.015 |
0.003 |
-0.073 |
| SMC |
0.9 |
0.015 |
0.013 |
0.003 |
0.570 |
| SMC |
0.99 |
0.014 |
0.014 |
0.006 |
-0.010 |
| Metro |
0.0 |
0.022 |
0.014 |
0.001 |
5.526 |
| Metro |
0.3 |
0.033 |
0.014 |
0.001 |
13.947 |
| Metro |
0.5 |
0.071 |
0.015 |
0.003 |
20.551 |
| Metro |
0.9 |
0.244 |
0.013 |
0.003 |
77.732 |
| Metro |
0.99 |
0.755 |
0.014 |
0.006 |
125.394 |
| DEMetro_Z |
0.0 |
0.939 |
0.014 |
0.001 |
650.738 |
| DEMetro_Z |
0.3 |
0.936 |
0.014 |
0.001 |
668.194 |
| DEMetro_Z |
0.5 |
0.956 |
0.015 |
0.003 |
345.227 |
| DEMetro_Z |
0.9 |
0.973 |
0.013 |
0.003 |
322.554 |
| DEMetro_Z |
0.99 |
0.916 |
0.014 |
0.006 |
152.700 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_heavy_Tails
(MvStudentT,
correlation,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.086 |
0.932 |
0.025 |
| HMC |
0.3 |
1.609 |
0.117 |
0.628 |
| HMC |
0.5 |
1.053 |
0.3 |
0.406 |
| HMC |
0.9 |
2.511 |
0.0174 |
1.089 |
| HMC |
0.99 |
1.568 |
0.126 |
0.612 |
| SMC |
0.0 |
3.996 |
0.000352 |
1.666 |
| SMC |
0.3 |
1.935 |
0.0621 |
0.844 |
| SMC |
0.5 |
6.218 |
1.02e-06 |
3.104 |
| SMC |
0.9 |
3.371 |
0.00194 |
1.387 |
| SMC |
0.99 |
2.629 |
0.0133 |
1.173 |
| Metro |
0.0 |
1.573 |
0.132 |
2.512 |
| Metro |
0.3 |
1.600 |
0.126 |
3.763 |
| Metro |
0.5 |
3.295 |
0.00284 |
1.829 |
| Metro |
0.9 |
3.124 |
0.00525 |
3.663 |
| Metro |
0.99 |
4.815 |
0.000118 |
20.176 |
| DEMetro_Z |
0.0 |
3.563 |
0.00147 |
2.032 |
| DEMetro_Z |
0.3 |
4.652 |
0.000115 |
3.511 |
| DEMetro_Z |
0.5 |
2.717 |
0.0133 |
3.751 |
| DEMetro_Z |
0.9 |
4.279 |
0.000297 |
3.357 |
| DEMetro_Z |
0.99 |
2.746 |
0.0118 |
2.227 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-3.555
|
0.00211
|
-0.795
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.280
|
0.00394
|
-0.733
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.326
|
0.0313
|
-0.520
|
| HMC_vs_DEMetro_Z |
0.9
|
-3.001
|
0.00735
|
-0.671
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.085
|
0.0508
|
-0.466
|
| Metro_vs_SMC |
0.0
|
0.521
|
0.608
|
0.116
|
| Metro_vs_SMC |
0.3
|
1.250
|
0.226
|
0.280
|
| Metro_vs_SMC |
0.5
|
-1.570
|
0.133
|
-0.351
|
| Metro_vs_SMC |
0.9
|
1.841
|
0.0813
|
0.412
|
| Metro_vs_SMC |
0.99
|
4.533
|
0.000228
|
1.013
|
| Metro_vs_DEMetro_Z |
0.0
|
0.284
|
0.779
|
0.064
|
| Metro_vs_DEMetro_Z |
0.3
|
0.099
|
0.922
|
0.022
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.740
|
0.098
|
-0.389
|
| Metro_vs_DEMetro_Z |
0.9
|
0.210
|
0.836
|
0.047
|
| Metro_vs_DEMetro_Z |
0.99
|
4.372
|
0.000328
|
0.978
|
| HMC_vs_Metro |
0.0
|
-1.602
|
0.126
|
-0.358
|
| HMC_vs_Metro |
0.3
|
-1.334
|
0.198
|
-0.298
|
| HMC_vs_Metro |
0.5
|
-2.280
|
0.0343
|
-0.510
|
| HMC_vs_Metro |
0.9
|
-2.163
|
0.0435
|
-0.484
|
| HMC_vs_Metro |
0.99
|
-4.647
|
0.000176
|
-1.039
|
| HMC_vs_SMC |
0.0
|
-5.107
|
6.26e-05
|
-1.142
|
| HMC_vs_SMC |
0.3
|
-0.363
|
0.721
|
-0.081
|
| HMC_vs_SMC |
0.5
|
-4.675
|
0.000165
|
-1.045
|
| HMC_vs_SMC |
0.9
|
-0.657
|
0.519
|
-0.147
|
| HMC_vs_SMC |
0.99
|
-1.107
|
0.282
|
-0.247
|
| DEMetro_Z_vs_SMC |
0.0
|
0.559
|
0.583
|
0.125
|
| DEMetro_Z_vs_SMC |
0.3
|
3.461
|
0.00262
|
0.774
|
| DEMetro_Z_vs_SMC |
0.5
|
0.445
|
0.661
|
0.100
|
| DEMetro_Z_vs_SMC |
0.9
|
2.381
|
0.0279
|
0.532
|
| DEMetro_Z_vs_SMC |
0.99
|
1.168
|
0.257
|
0.261
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.067 |
0.066 |
0.039 |
0.025 |
| HMC |
0.3 |
0.059 |
0.045 |
0.023 |
0.628 |
| HMC |
0.5 |
0.080 |
0.062 |
0.045 |
0.406 |
| HMC |
0.9 |
0.103 |
0.055 |
0.044 |
1.089 |
| HMC |
0.99 |
0.092 |
0.060 |
0.052 |
0.612 |
| SMC |
0.0 |
0.132 |
0.066 |
0.039 |
1.666 |
| SMC |
0.3 |
0.064 |
0.045 |
0.023 |
0.844 |
| SMC |
0.5 |
0.201 |
0.062 |
0.045 |
3.104 |
| SMC |
0.9 |
0.117 |
0.055 |
0.044 |
1.387 |
| SMC |
0.99 |
0.121 |
0.060 |
0.052 |
1.173 |
| Metro |
0.0 |
0.165 |
0.066 |
0.039 |
2.512 |
| Metro |
0.3 |
0.131 |
0.045 |
0.023 |
3.763 |
| Metro |
0.5 |
0.144 |
0.062 |
0.045 |
1.829 |
| Metro |
0.9 |
0.217 |
0.055 |
0.044 |
3.663 |
| Metro |
0.99 |
1.105 |
0.060 |
0.052 |
20.176 |
| DEMetro_Z |
0.0 |
0.146 |
0.066 |
0.039 |
2.032 |
| DEMetro_Z |
0.3 |
0.125 |
0.045 |
0.023 |
3.511 |
| DEMetro_Z |
0.5 |
0.230 |
0.062 |
0.045 |
3.751 |
| DEMetro_Z |
0.9 |
0.203 |
0.055 |
0.044 |
3.357 |
| DEMetro_Z |
0.99 |
0.176 |
0.060 |
0.052 |
2.227 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.780 |
0.441 |
-0.201 |
| HMC |
0.3 |
-0.699 |
0.491 |
-0.169 |
| HMC |
0.5 |
0.359 |
0.723 |
0.196 |
| HMC |
0.9 |
1.429 |
0.169 |
11.089 |
| HMC |
0.99 |
-0.061 |
0.952 |
-0.018 |
| SMC |
0.0 |
1.411 |
0.169 |
0.356 |
| SMC |
0.3 |
0.768 |
0.449 |
0.189 |
| SMC |
0.5 |
8.666 |
4.4e-09 |
4.980 |
| SMC |
0.9 |
2.461 |
0.0236 |
16.080 |
| SMC |
0.99 |
3.873 |
0.000423 |
1.135 |
| Metro |
0.0 |
0.514 |
0.611 |
0.205 |
| Metro |
0.3 |
0.433 |
0.667 |
0.135 |
| Metro |
0.5 |
0.021 |
0.984 |
0.011 |
| Metro |
0.9 |
1.240 |
0.23 |
9.471 |
| Metro |
0.99 |
1.949 |
0.0609 |
0.909 |
| DEMetro_Z |
0.0 |
-0.509 |
0.614 |
-0.136 |
| DEMetro_Z |
0.3 |
-0.098 |
0.923 |
-0.024 |
| DEMetro_Z |
0.5 |
1.054 |
0.305 |
2.507 |
| DEMetro_Z |
0.9 |
1.323 |
0.202 |
10.220 |
| DEMetro_Z |
0.99 |
-0.709 |
0.486 |
-0.163 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-4.234
|
0.000449
|
-0.947
|
| HMC_vs_SMC |
0.3
|
-2.313
|
0.0321
|
-0.517
|
| HMC_vs_SMC |
0.5
|
-6.627
|
2.43e-06
|
-1.482
|
| HMC_vs_SMC |
0.9
|
-1.973
|
0.0632
|
-0.441
|
| HMC_vs_SMC |
0.99
|
-4.750
|
0.000139
|
-1.062
|
| Metro_vs_DEMetro_Z |
0.0
|
1.099
|
0.286
|
0.246
|
| Metro_vs_DEMetro_Z |
0.3
|
0.778
|
0.446
|
0.174
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.061
|
0.302
|
-0.237
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.433
|
0.67
|
-0.097
|
| Metro_vs_DEMetro_Z |
0.99
|
2.595
|
0.0178
|
0.580
|
| HMC_vs_Metro |
0.0
|
-1.273
|
0.218
|
-0.285
|
| HMC_vs_Metro |
0.3
|
-1.487
|
0.153
|
-0.333
|
| HMC_vs_Metro |
0.5
|
1.405
|
0.176
|
0.314
|
| HMC_vs_Metro |
0.9
|
0.738
|
0.47
|
0.165
|
| HMC_vs_Metro |
0.99
|
-1.881
|
0.0754
|
-0.421
|
| HMC_vs_DEMetro_Z |
0.0
|
-1.012
|
0.324
|
-0.226
|
| HMC_vs_DEMetro_Z |
0.3
|
-5.112
|
6.19e-05
|
-1.143
|
| HMC_vs_DEMetro_Z |
0.5
|
-0.984
|
0.337
|
-0.220
|
| HMC_vs_DEMetro_Z |
0.9
|
0.868
|
0.396
|
0.194
|
| HMC_vs_DEMetro_Z |
0.99
|
0.766
|
0.453
|
0.171
|
| Metro_vs_SMC |
0.0
|
-0.415
|
0.683
|
-0.093
|
| Metro_vs_SMC |
0.3
|
-0.210
|
0.836
|
-0.047
|
| Metro_vs_SMC |
0.5
|
-7.072
|
9.94e-07
|
-1.581
|
| Metro_vs_SMC |
0.9
|
-3.634
|
0.00177
|
-0.813
|
| Metro_vs_SMC |
0.99
|
-0.505
|
0.619
|
-0.113
|
| DEMetro_Z_vs_SMC |
0.0
|
-2.918
|
0.00881
|
-0.653
|
| DEMetro_Z_vs_SMC |
0.3
|
-1.329
|
0.199
|
-0.297
|
| DEMetro_Z_vs_SMC |
0.5
|
-1.050
|
0.307
|
-0.235
|
| DEMetro_Z_vs_SMC |
0.9
|
-2.856
|
0.0101
|
-0.639
|
| DEMetro_Z_vs_SMC |
0.99
|
-6.207
|
5.8e-06
|
-1.388
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
6.243 |
9.309 |
15.244 |
-0.201 |
| HMC |
0.3 |
4.677 |
6.558 |
11.160 |
-0.169 |
| HMC |
0.5 |
9.380 |
7.776 |
8.203 |
0.196 |
| HMC |
0.9 |
21.206 |
2.247 |
1.710 |
11.089 |
| HMC |
0.99 |
7.300 |
7.581 |
15.891 |
-0.018 |
| SMC |
0.0 |
14.740 |
9.309 |
15.244 |
0.356 |
| SMC |
0.3 |
8.667 |
6.558 |
11.160 |
0.189 |
| SMC |
0.5 |
48.624 |
7.776 |
8.203 |
4.980 |
| SMC |
0.9 |
29.738 |
2.247 |
1.710 |
16.080 |
| SMC |
0.99 |
25.613 |
7.581 |
15.891 |
1.135 |
| Metro |
0.0 |
12.441 |
9.309 |
15.244 |
0.205 |
| Metro |
0.3 |
8.060 |
6.558 |
11.160 |
0.135 |
| Metro |
0.5 |
7.870 |
7.776 |
8.203 |
0.011 |
| Metro |
0.9 |
18.440 |
2.247 |
1.710 |
9.471 |
| Metro |
0.99 |
22.019 |
7.581 |
15.891 |
0.909 |
| DEMetro_Z |
0.0 |
7.237 |
9.309 |
15.244 |
-0.136 |
| DEMetro_Z |
0.3 |
6.295 |
6.558 |
11.160 |
-0.024 |
| DEMetro_Z |
0.5 |
28.338 |
7.776 |
8.203 |
2.507 |
| DEMetro_Z |
0.9 |
19.720 |
2.247 |
1.710 |
10.220 |
| DEMetro_Z |
0.99 |
4.997 |
7.581 |
15.891 |
-0.163 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.935 |
0.0606 |
0.633 |
| HMC |
0.3 |
2.819 |
0.00857 |
1.332 |
| HMC |
0.5 |
2.582 |
0.0148 |
1.136 |
| HMC |
0.9 |
3.431 |
0.00253 |
3.529 |
| HMC |
0.99 |
3.512 |
0.00156 |
1.804 |
| SMC |
0.0 |
9.996 |
4.1e-09 |
19.627 |
| SMC |
0.3 |
9.422 |
1.14e-08 |
21.260 |
| SMC |
0.5 |
13.994 |
1.69e-11 |
56.364 |
| SMC |
0.9 |
11.097 |
8.56e-10 |
35.040 |
| SMC |
0.99 |
10.770 |
1.38e-09 |
31.461 |
| Metro |
0.0 |
3.554 |
0.00198 |
4.804 |
| Metro |
0.3 |
2.929 |
0.00844 |
5.620 |
| Metro |
0.5 |
7.101 |
1.42e-07 |
3.880 |
| Metro |
0.9 |
5.703 |
1.43e-05 |
8.413 |
| Metro |
0.99 |
5.851 |
1.22e-05 |
35.993 |
| DEMetro_Z |
0.0 |
8.441 |
2.09e-09 |
3.857 |
| DEMetro_Z |
0.3 |
11.037 |
3.32e-11 |
6.375 |
| DEMetro_Z |
0.5 |
2.230 |
0.0379 |
11.429 |
| DEMetro_Z |
0.9 |
5.092 |
5.64e-05 |
7.433 |
| DEMetro_Z |
0.99 |
6.765 |
6.88e-07 |
4.940 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
0.689
|
0.499
|
0.154
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.375
|
0.712
|
-0.084
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.532
|
0.142
|
-0.343
|
| Metro_vs_DEMetro_Z |
0.9
|
0.447
|
0.66
|
0.100
|
| Metro_vs_DEMetro_Z |
0.99
|
5.276
|
4.31e-05
|
1.180
|
| DEMetro_Z_vs_SMC |
0.0
|
-7.447
|
4.78e-07
|
-1.665
|
| DEMetro_Z_vs_SMC |
0.3
|
-5.896
|
1.12e-05
|
-1.318
|
| DEMetro_Z_vs_SMC |
0.5
|
-7.673
|
3.1e-07
|
-1.716
|
| DEMetro_Z_vs_SMC |
0.9
|
-8.643
|
5.22e-08
|
-1.933
|
| DEMetro_Z_vs_SMC |
0.99
|
-8.376
|
8.42e-08
|
-1.873
|
| HMC_vs_DEMetro_Z |
0.0
|
-7.962
|
1.8e-07
|
-1.780
|
| HMC_vs_DEMetro_Z |
0.3
|
-6.908
|
1.38e-06
|
-1.545
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.010
|
0.0588
|
-0.450
|
| HMC_vs_DEMetro_Z |
0.9
|
-3.593
|
0.00194
|
-0.803
|
| HMC_vs_DEMetro_Z |
0.99
|
-3.454
|
0.00266
|
-0.772
|
| HMC_vs_Metro |
0.0
|
-3.170
|
0.00504
|
-0.709
|
| HMC_vs_Metro |
0.3
|
-2.254
|
0.0362
|
-0.504
|
| HMC_vs_Metro |
0.5
|
-6.387
|
3.98e-06
|
-1.428
|
| HMC_vs_Metro |
0.9
|
-2.753
|
0.0127
|
-0.615
|
| HMC_vs_Metro |
0.99
|
-5.422
|
3.13e-05
|
-1.212
|
| HMC_vs_SMC |
0.0
|
-10.070
|
4.7e-09
|
-2.252
|
| HMC_vs_SMC |
0.3
|
-8.479
|
6.99e-08
|
-1.896
|
| HMC_vs_SMC |
0.5
|
-13.349
|
4.2e-11
|
-2.985
|
| HMC_vs_SMC |
0.9
|
-9.359
|
1.51e-08
|
-2.093
|
| HMC_vs_SMC |
0.99
|
-10.574
|
2.12e-09
|
-2.364
|
| Metro_vs_SMC |
0.0
|
-5.423
|
3.12e-05
|
-1.213
|
| Metro_vs_SMC |
0.3
|
-5.129
|
5.97e-05
|
-1.147
|
| Metro_vs_SMC |
0.5
|
-12.958
|
7.01e-11
|
-2.897
|
| Metro_vs_SMC |
0.9
|
-7.676
|
3.08e-07
|
-1.717
|
| Metro_vs_SMC |
0.99
|
0.641
|
0.529
|
0.143
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.148 |
0.124 |
0.038 |
0.633 |
| HMC |
0.3 |
0.146 |
0.115 |
0.024 |
1.332 |
| HMC |
0.5 |
0.162 |
0.123 |
0.034 |
1.136 |
| HMC |
0.9 |
0.210 |
0.106 |
0.029 |
3.529 |
| HMC |
0.99 |
0.195 |
0.119 |
0.042 |
1.804 |
| SMC |
0.0 |
0.863 |
0.124 |
0.038 |
19.627 |
| SMC |
0.3 |
0.615 |
0.115 |
0.024 |
21.260 |
| SMC |
0.5 |
2.057 |
0.123 |
0.034 |
56.364 |
| SMC |
0.9 |
1.131 |
0.106 |
0.029 |
35.040 |
| SMC |
0.99 |
1.436 |
0.119 |
0.042 |
31.461 |
| Metro |
0.0 |
0.305 |
0.124 |
0.038 |
4.804 |
| Metro |
0.3 |
0.247 |
0.115 |
0.024 |
5.620 |
| Metro |
0.5 |
0.256 |
0.123 |
0.034 |
3.880 |
| Metro |
0.9 |
0.352 |
0.106 |
0.029 |
8.413 |
| Metro |
0.99 |
1.626 |
0.119 |
0.042 |
35.993 |
| DEMetro_Z |
0.0 |
0.269 |
0.124 |
0.038 |
3.857 |
| DEMetro_Z |
0.3 |
0.265 |
0.115 |
0.024 |
6.375 |
| DEMetro_Z |
0.5 |
0.515 |
0.123 |
0.034 |
11.429 |
| DEMetro_Z |
0.9 |
0.324 |
0.106 |
0.029 |
7.433 |
| DEMetro_Z |
0.99 |
0.326 |
0.119 |
0.042 |
4.940 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.691 |
0.0118 |
1.327 |
| HMC |
0.3 |
2.393 |
0.024 |
1.284 |
| HMC |
0.5 |
2.876 |
0.00667 |
1.004 |
| HMC |
0.9 |
4.124 |
0.000353 |
2.411 |
| HMC |
0.99 |
4.770 |
4.7e-05 |
2.236 |
| SMC |
0.0 |
12.676 |
8.09e-11 |
30.347 |
| SMC |
0.3 |
11.681 |
3.3e-10 |
28.025 |
| SMC |
0.5 |
20.633 |
1.48e-14 |
68.089 |
| SMC |
0.9 |
14.484 |
8.82e-12 |
47.536 |
| SMC |
0.99 |
14.681 |
6.57e-12 |
40.991 |
| Metro |
0.0 |
9.504 |
6.22e-10 |
5.334 |
| Metro |
0.3 |
5.615 |
9.89e-06 |
3.936 |
| Metro |
0.5 |
7.603 |
1.85e-07 |
7.602 |
| Metro |
0.9 |
8.601 |
3.58e-08 |
11.413 |
| Metro |
0.99 |
8.717 |
4.46e-08 |
47.588 |
| DEMetro_Z |
0.0 |
9.169 |
2.25e-09 |
5.768 |
| DEMetro_Z |
0.3 |
7.495 |
2.09e-07 |
6.978 |
| DEMetro_Z |
0.5 |
5.186 |
4.9e-05 |
10.819 |
| DEMetro_Z |
0.9 |
9.618 |
2.48e-09 |
7.975 |
| DEMetro_Z |
0.99 |
7.346 |
2.49e-07 |
6.246 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
-9.351
|
1.53e-08
|
-2.091
|
| DEMetro_Z_vs_SMC |
0.3
|
-7.067
|
1e-06
|
-1.580
|
| DEMetro_Z_vs_SMC |
0.5
|
-18.216
|
1.73e-13
|
-4.073
|
| DEMetro_Z_vs_SMC |
0.9
|
-12.763
|
9.08e-11
|
-2.854
|
| DEMetro_Z_vs_SMC |
0.99
|
-11.152
|
8.84e-10
|
-2.494
|
| HMC_vs_Metro |
0.0
|
-5.703
|
1.69e-05
|
-1.275
|
| HMC_vs_Metro |
0.3
|
-3.385
|
0.00311
|
-0.757
|
| HMC_vs_Metro |
0.5
|
-6.399
|
3.89e-06
|
-1.431
|
| HMC_vs_Metro |
0.9
|
-6.457
|
3.45e-06
|
-1.444
|
| HMC_vs_Metro |
0.99
|
-8.404
|
8e-08
|
-1.879
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.703
|
0.49
|
-0.157
|
| Metro_vs_DEMetro_Z |
0.3
|
-2.495
|
0.022
|
-0.558
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.264
|
0.222
|
-0.283
|
| Metro_vs_DEMetro_Z |
0.9
|
1.957
|
0.0652
|
0.438
|
| Metro_vs_DEMetro_Z |
0.99
|
7.749
|
2.68e-07
|
1.733
|
| HMC_vs_SMC |
0.0
|
-12.080
|
2.31e-10
|
-2.701
|
| HMC_vs_SMC |
0.3
|
-10.833
|
1.43e-09
|
-2.422
|
| HMC_vs_SMC |
0.5
|
-20.461
|
2.1e-14
|
-4.575
|
| HMC_vs_SMC |
0.9
|
-13.460
|
3.64e-11
|
-3.010
|
| HMC_vs_SMC |
0.99
|
-13.994
|
1.86e-11
|
-3.129
|
| Metro_vs_SMC |
0.0
|
-9.719
|
8.31e-09
|
-2.173
|
| Metro_vs_SMC |
0.3
|
-10.093
|
4.53e-09
|
-2.257
|
| Metro_vs_SMC |
0.5
|
-17.540
|
3.41e-13
|
-3.922
|
| Metro_vs_SMC |
0.9
|
-11.236
|
7.8e-10
|
-2.513
|
| Metro_vs_SMC |
0.99
|
0.993
|
0.333
|
0.222
|
| HMC_vs_DEMetro_Z |
0.0
|
-7.206
|
7.64e-07
|
-1.611
|
| HMC_vs_DEMetro_Z |
0.3
|
-5.031
|
7.41e-05
|
-1.125
|
| HMC_vs_DEMetro_Z |
0.5
|
-4.560
|
0.000214
|
-1.020
|
| HMC_vs_DEMetro_Z |
0.9
|
-5.424
|
3.11e-05
|
-1.213
|
| HMC_vs_DEMetro_Z |
0.99
|
-5.300
|
4.09e-05
|
-1.185
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.021 |
0.014 |
0.005 |
1.327 |
| HMC |
0.3 |
0.020 |
0.015 |
0.004 |
1.284 |
| HMC |
0.5 |
0.019 |
0.015 |
0.004 |
1.004 |
| HMC |
0.9 |
0.023 |
0.013 |
0.004 |
2.411 |
| HMC |
0.99 |
0.028 |
0.015 |
0.006 |
2.236 |
| SMC |
0.0 |
0.156 |
0.014 |
0.005 |
30.347 |
| SMC |
0.3 |
0.121 |
0.015 |
0.004 |
28.025 |
| SMC |
0.5 |
0.282 |
0.015 |
0.004 |
68.089 |
| SMC |
0.9 |
0.194 |
0.013 |
0.004 |
47.536 |
| SMC |
0.99 |
0.246 |
0.015 |
0.006 |
40.991 |
| Metro |
0.0 |
0.039 |
0.014 |
0.005 |
5.334 |
| Metro |
0.3 |
0.030 |
0.015 |
0.004 |
3.936 |
| Metro |
0.5 |
0.045 |
0.015 |
0.004 |
7.602 |
| Metro |
0.9 |
0.057 |
0.013 |
0.004 |
11.413 |
| Metro |
0.99 |
0.283 |
0.015 |
0.006 |
47.588 |
| DEMetro_Z |
0.0 |
0.041 |
0.014 |
0.005 |
5.768 |
| DEMetro_Z |
0.3 |
0.041 |
0.015 |
0.004 |
6.978 |
| DEMetro_Z |
0.5 |
0.057 |
0.015 |
0.004 |
10.819 |
| DEMetro_Z |
0.9 |
0.044 |
0.013 |
0.004 |
7.975 |
| DEMetro_Z |
0.99 |
0.050 |
0.015 |
0.006 |
6.246 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.237 |
0.814 |
0.075 |
| HMC |
0.3 |
2.391 |
0.0264 |
2.592 |
| HMC |
0.5 |
-0.122 |
0.904 |
-0.038 |
| HMC |
0.9 |
2.081 |
0.0465 |
1.003 |
| HMC |
0.99 |
1.520 |
0.139 |
0.712 |
| SMC |
0.0 |
1.835 |
0.0765 |
0.838 |
| SMC |
0.3 |
3.022 |
0.00559 |
1.694 |
| SMC |
0.5 |
4.351 |
0.000266 |
3.846 |
| SMC |
0.9 |
2.276 |
0.0295 |
0.927 |
| SMC |
0.99 |
2.619 |
0.0143 |
1.381 |
| Metro |
0.0 |
2.963 |
0.00536 |
1.064 |
| Metro |
0.3 |
3.038 |
0.00626 |
3.067 |
| Metro |
0.5 |
3.827 |
0.000657 |
1.878 |
| Metro |
0.9 |
3.713 |
0.00129 |
3.718 |
| Metro |
0.99 |
1.792 |
0.089 |
74.629 |
| DEMetro_Z |
0.0 |
3.120 |
0.00473 |
2.117 |
| DEMetro_Z |
0.3 |
3.154 |
0.00501 |
4.603 |
| DEMetro_Z |
0.5 |
2.826 |
0.00988 |
2.406 |
| DEMetro_Z |
0.9 |
3.014 |
0.00622 |
2.220 |
| DEMetro_Z |
0.99 |
2.553 |
0.0173 |
1.566 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-3.200
|
0.00471
|
-0.716
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.872
|
0.0767
|
-0.418
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.119
|
0.00565
|
-0.697
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.369
|
0.187
|
-0.306
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.134
|
0.271
|
-0.254
|
| Metro_vs_SMC |
0.0
|
0.565
|
0.579
|
0.126
|
| Metro_vs_SMC |
0.3
|
1.129
|
0.273
|
0.253
|
| Metro_vs_SMC |
0.5
|
-2.177
|
0.0423
|
-0.487
|
| Metro_vs_SMC |
0.9
|
2.986
|
0.0076
|
0.668
|
| Metro_vs_SMC |
0.99
|
1.761
|
0.0944
|
0.394
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.439
|
0.167
|
-0.322
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.900
|
0.379
|
-0.201
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.568
|
0.577
|
-0.127
|
| Metro_vs_DEMetro_Z |
0.9
|
1.156
|
0.262
|
0.259
|
| Metro_vs_DEMetro_Z |
0.99
|
1.757
|
0.0951
|
0.393
|
| HMC_vs_Metro |
0.0
|
-2.521
|
0.0208
|
-0.564
|
| HMC_vs_Metro |
0.3
|
-0.377
|
0.71
|
-0.084
|
| HMC_vs_Metro |
0.5
|
-3.857
|
0.00106
|
-0.862
|
| HMC_vs_Metro |
0.9
|
-2.506
|
0.0215
|
-0.560
|
| HMC_vs_Metro |
0.99
|
-1.782
|
0.0908
|
-0.398
|
| HMC_vs_SMC |
0.0
|
-1.528
|
0.143
|
-0.342
|
| HMC_vs_SMC |
0.3
|
0.651
|
0.523
|
0.145
|
| HMC_vs_SMC |
0.5
|
-4.300
|
0.000386
|
-0.962
|
| HMC_vs_SMC |
0.9
|
0.144
|
0.887
|
0.032
|
| HMC_vs_SMC |
0.99
|
-1.146
|
0.266
|
-0.256
|
| DEMetro_Z_vs_SMC |
0.0
|
1.634
|
0.119
|
0.365
|
| DEMetro_Z_vs_SMC |
0.3
|
1.661
|
0.113
|
0.371
|
| DEMetro_Z_vs_SMC |
0.5
|
-1.105
|
0.283
|
-0.247
|
| DEMetro_Z_vs_SMC |
0.9
|
1.806
|
0.0868
|
0.404
|
| DEMetro_Z_vs_SMC |
0.99
|
0.219
|
0.829
|
0.049
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.069 |
0.066 |
0.039 |
0.075 |
| HMC |
0.3 |
0.104 |
0.045 |
0.023 |
2.592 |
| HMC |
0.5 |
0.060 |
0.062 |
0.045 |
-0.038 |
| HMC |
0.9 |
0.100 |
0.055 |
0.044 |
1.003 |
| HMC |
0.99 |
0.097 |
0.060 |
0.052 |
0.712 |
| SMC |
0.0 |
0.099 |
0.066 |
0.039 |
0.838 |
| SMC |
0.3 |
0.084 |
0.045 |
0.023 |
1.694 |
| SMC |
0.5 |
0.234 |
0.062 |
0.045 |
3.846 |
| SMC |
0.9 |
0.096 |
0.055 |
0.044 |
0.927 |
| SMC |
0.99 |
0.132 |
0.060 |
0.052 |
1.381 |
| Metro |
0.0 |
0.108 |
0.066 |
0.039 |
1.064 |
| Metro |
0.3 |
0.115 |
0.045 |
0.023 |
3.067 |
| Metro |
0.5 |
0.146 |
0.062 |
0.045 |
1.878 |
| Metro |
0.9 |
0.219 |
0.055 |
0.044 |
3.718 |
| Metro |
0.99 |
3.926 |
0.060 |
0.052 |
74.629 |
| DEMetro_Z |
0.0 |
0.149 |
0.066 |
0.039 |
2.117 |
| DEMetro_Z |
0.3 |
0.150 |
0.045 |
0.023 |
4.603 |
| DEMetro_Z |
0.5 |
0.170 |
0.062 |
0.045 |
2.406 |
| DEMetro_Z |
0.9 |
0.153 |
0.055 |
0.044 |
2.220 |
| DEMetro_Z |
0.99 |
0.141 |
0.060 |
0.052 |
1.566 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.519 |
0.607 |
-0.142 |
| HMC |
0.3 |
-0.686 |
0.499 |
-0.163 |
| HMC |
0.5 |
-0.039 |
0.969 |
-0.022 |
| HMC |
0.9 |
1.344 |
0.195 |
10.580 |
| HMC |
0.99 |
-1.091 |
0.287 |
-0.252 |
| SMC |
0.0 |
-0.862 |
0.396 |
-0.213 |
| SMC |
0.3 |
-0.577 |
0.57 |
-0.136 |
| SMC |
0.5 |
2.625 |
0.0143 |
1.478 |
| SMC |
0.9 |
1.550 |
0.138 |
11.162 |
| SMC |
0.99 |
0.992 |
0.329 |
0.252 |
| Metro |
0.0 |
-0.769 |
0.447 |
-0.204 |
| Metro |
0.3 |
-0.401 |
0.692 |
-0.096 |
| Metro |
0.5 |
0.260 |
0.797 |
0.141 |
| Metro |
0.9 |
1.204 |
0.243 |
9.110 |
| Metro |
0.99 |
1.420 |
0.172 |
14.987 |
| DEMetro_Z |
0.0 |
-0.314 |
0.755 |
-0.084 |
| DEMetro_Z |
0.3 |
-0.101 |
0.921 |
-0.024 |
| DEMetro_Z |
0.5 |
0.153 |
0.879 |
0.083 |
| DEMetro_Z |
0.9 |
1.232 |
0.233 |
9.415 |
| DEMetro_Z |
0.99 |
-0.980 |
0.338 |
-0.227 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
0.895
|
0.382
|
0.200
|
| HMC_vs_SMC |
0.3
|
-0.558
|
0.583
|
-0.125
|
| HMC_vs_SMC |
0.5
|
-3.566
|
0.00206
|
-0.797
|
| HMC_vs_SMC |
0.9
|
-0.267
|
0.793
|
-0.060
|
| HMC_vs_SMC |
0.99
|
-3.854
|
0.00107
|
-0.862
|
| Metro_vs_DEMetro_Z |
0.0
|
-3.025
|
0.00696
|
-0.677
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.243
|
0.229
|
-0.278
|
| Metro_vs_DEMetro_Z |
0.5
|
0.640
|
0.53
|
0.143
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.523
|
0.607
|
-0.117
|
| Metro_vs_DEMetro_Z |
0.99
|
1.440
|
0.166
|
0.322
|
| HMC_vs_Metro |
0.0
|
0.793
|
0.438
|
0.177
|
| HMC_vs_Metro |
0.3
|
-1.729
|
0.1
|
-0.387
|
| HMC_vs_Metro |
0.5
|
-2.801
|
0.0114
|
-0.626
|
| HMC_vs_Metro |
0.9
|
0.763
|
0.455
|
0.171
|
| HMC_vs_Metro |
0.99
|
-1.442
|
0.165
|
-0.323
|
| HMC_vs_DEMetro_Z |
0.0
|
-0.651
|
0.523
|
-0.146
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.597
|
0.0177
|
-0.581
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.433
|
0.168
|
-0.320
|
| HMC_vs_DEMetro_Z |
0.9
|
0.580
|
0.568
|
0.130
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.763
|
0.455
|
-0.171
|
| Metro_vs_SMC |
0.0
|
0.132
|
0.896
|
0.030
|
| Metro_vs_SMC |
0.3
|
0.858
|
0.402
|
0.192
|
| Metro_vs_SMC |
0.5
|
-3.354
|
0.00334
|
-0.750
|
| Metro_vs_SMC |
0.9
|
-2.480
|
0.0227
|
-0.554
|
| Metro_vs_SMC |
0.99
|
1.394
|
0.18
|
0.312
|
| DEMetro_Z_vs_SMC |
0.0
|
1.616
|
0.123
|
0.361
|
| DEMetro_Z_vs_SMC |
0.3
|
1.392
|
0.18
|
0.311
|
| DEMetro_Z_vs_SMC |
0.5
|
-3.351
|
0.00336
|
-0.749
|
| DEMetro_Z_vs_SMC |
0.9
|
-1.585
|
0.129
|
-0.354
|
| DEMetro_Z_vs_SMC |
0.99
|
-3.439
|
0.00275
|
-0.769
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
7.150 |
9.309 |
15.244 |
-0.142 |
| HMC |
0.3 |
4.738 |
6.558 |
11.160 |
-0.163 |
| HMC |
0.5 |
7.599 |
7.776 |
8.203 |
-0.022 |
| HMC |
0.9 |
20.335 |
2.247 |
1.710 |
10.580 |
| HMC |
0.99 |
3.575 |
7.581 |
15.891 |
-0.252 |
| SMC |
0.0 |
6.060 |
9.309 |
15.244 |
-0.213 |
| SMC |
0.3 |
5.042 |
6.558 |
11.160 |
-0.136 |
| SMC |
0.5 |
19.897 |
7.776 |
8.203 |
1.478 |
| SMC |
0.9 |
21.330 |
2.247 |
1.710 |
11.162 |
| SMC |
0.99 |
11.591 |
7.581 |
15.891 |
0.252 |
| Metro |
0.0 |
6.194 |
9.309 |
15.244 |
-0.204 |
| Metro |
0.3 |
5.488 |
6.558 |
11.160 |
-0.096 |
| Metro |
0.5 |
8.933 |
7.776 |
8.203 |
0.141 |
| Metro |
0.9 |
17.822 |
2.247 |
1.710 |
9.110 |
| Metro |
0.99 |
245.732 |
7.581 |
15.891 |
14.987 |
| DEMetro_Z |
0.0 |
8.031 |
9.309 |
15.244 |
-0.084 |
| DEMetro_Z |
0.3 |
6.286 |
6.558 |
11.160 |
-0.024 |
| DEMetro_Z |
0.5 |
8.456 |
7.776 |
8.203 |
0.083 |
| DEMetro_Z |
0.9 |
18.344 |
2.247 |
1.710 |
9.415 |
| DEMetro_Z |
0.99 |
3.979 |
7.581 |
15.891 |
-0.227 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.246 |
0.0306 |
0.740 |
| HMC |
0.3 |
2.646 |
0.0153 |
3.125 |
| HMC |
0.5 |
2.478 |
0.018 |
0.881 |
| HMC |
0.9 |
4.300 |
0.000285 |
3.438 |
| HMC |
0.99 |
3.530 |
0.00136 |
1.607 |
| SMC |
0.0 |
5.450 |
2.52e-05 |
8.123 |
| SMC |
0.3 |
5.039 |
6.77e-05 |
10.027 |
| SMC |
0.5 |
7.171 |
7.89e-07 |
28.875 |
| SMC |
0.9 |
7.409 |
4.56e-07 |
16.842 |
| SMC |
0.99 |
6.864 |
1.37e-06 |
16.573 |
| Metro |
0.0 |
6.589 |
9.16e-08 |
2.003 |
| Metro |
0.3 |
4.309 |
0.000325 |
4.946 |
| Metro |
0.5 |
6.591 |
6.76e-07 |
3.978 |
| Metro |
0.9 |
9.789 |
2.48e-09 |
9.216 |
| Metro |
0.99 |
1.912 |
0.071 |
100.681 |
| DEMetro_Z |
0.0 |
7.979 |
1.99e-08 |
4.531 |
| DEMetro_Z |
0.3 |
4.381 |
0.000297 |
7.175 |
| DEMetro_Z |
0.5 |
6.138 |
3.67e-06 |
5.219 |
| DEMetro_Z |
0.9 |
7.310 |
2.78e-07 |
6.337 |
| DEMetro_Z |
0.99 |
5.045 |
3.63e-05 |
3.223 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-4.612
|
0.00019
|
-1.031
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.078
|
0.295
|
-0.241
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.058
|
0.303
|
-0.237
|
| Metro_vs_DEMetro_Z |
0.9
|
1.986
|
0.0617
|
0.444
|
| Metro_vs_DEMetro_Z |
0.99
|
1.848
|
0.0803
|
0.413
|
| DEMetro_Z_vs_SMC |
0.0
|
-2.266
|
0.0353
|
-0.507
|
| DEMetro_Z_vs_SMC |
0.3
|
-0.987
|
0.336
|
-0.221
|
| DEMetro_Z_vs_SMC |
0.5
|
-5.526
|
2.49e-05
|
-1.236
|
| DEMetro_Z_vs_SMC |
0.9
|
-4.342
|
0.000351
|
-0.971
|
| DEMetro_Z_vs_SMC |
0.99
|
-5.355
|
3.62e-05
|
-1.197
|
| HMC_vs_DEMetro_Z |
0.0
|
-7.155
|
8.44e-07
|
-1.600
|
| HMC_vs_DEMetro_Z |
0.3
|
-2.755
|
0.0126
|
-0.616
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.749
|
1.54e-05
|
-1.286
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.409
|
0.0263
|
-0.539
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.041
|
0.0554
|
-0.456
|
| HMC_vs_Metro |
0.0
|
-3.839
|
0.00111
|
-0.858
|
| HMC_vs_Metro |
0.3
|
-1.127
|
0.274
|
-0.252
|
| HMC_vs_Metro |
0.5
|
-4.669
|
0.000167
|
-1.044
|
| HMC_vs_Metro |
0.9
|
-4.936
|
9.18e-05
|
-1.104
|
| HMC_vs_Metro |
0.99
|
-1.884
|
0.075
|
-0.421
|
| HMC_vs_SMC |
0.0
|
-5.258
|
4.48e-05
|
-1.176
|
| HMC_vs_SMC |
0.3
|
-2.756
|
0.0126
|
-0.616
|
| HMC_vs_SMC |
0.5
|
-7.025
|
1.09e-06
|
-1.571
|
| HMC_vs_SMC |
0.9
|
-5.543
|
2.4e-05
|
-1.239
|
| HMC_vs_SMC |
0.99
|
-6.401
|
3.87e-06
|
-1.431
|
| Metro_vs_SMC |
0.0
|
-4.279
|
0.000405
|
-0.957
|
| Metro_vs_SMC |
0.3
|
-2.161
|
0.0437
|
-0.483
|
| Metro_vs_SMC |
0.5
|
-6.515
|
3.06e-06
|
-1.457
|
| Metro_vs_SMC |
0.9
|
-3.746
|
0.00137
|
-0.838
|
| Metro_vs_SMC |
0.99
|
1.570
|
0.133
|
0.351
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.152 |
0.124 |
0.038 |
0.740 |
| HMC |
0.3 |
0.189 |
0.115 |
0.024 |
3.125 |
| HMC |
0.5 |
0.153 |
0.123 |
0.034 |
0.881 |
| HMC |
0.9 |
0.207 |
0.106 |
0.029 |
3.438 |
| HMC |
0.99 |
0.186 |
0.119 |
0.042 |
1.607 |
| SMC |
0.0 |
0.430 |
0.124 |
0.038 |
8.123 |
| SMC |
0.3 |
0.351 |
0.115 |
0.024 |
10.027 |
| SMC |
0.5 |
1.114 |
0.123 |
0.034 |
28.875 |
| SMC |
0.9 |
0.599 |
0.106 |
0.029 |
16.842 |
| SMC |
0.99 |
0.813 |
0.119 |
0.042 |
16.573 |
| Metro |
0.0 |
0.200 |
0.124 |
0.038 |
2.003 |
| Metro |
0.3 |
0.231 |
0.115 |
0.024 |
4.946 |
| Metro |
0.5 |
0.260 |
0.123 |
0.034 |
3.978 |
| Metro |
0.9 |
0.376 |
0.106 |
0.029 |
9.216 |
| Metro |
0.99 |
4.333 |
0.119 |
0.042 |
100.681 |
| DEMetro_Z |
0.0 |
0.295 |
0.124 |
0.038 |
4.531 |
| DEMetro_Z |
0.3 |
0.284 |
0.115 |
0.024 |
7.175 |
| DEMetro_Z |
0.5 |
0.302 |
0.123 |
0.034 |
5.219 |
| DEMetro_Z |
0.9 |
0.292 |
0.106 |
0.029 |
6.337 |
| DEMetro_Z |
0.99 |
0.254 |
0.119 |
0.042 |
3.223 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.653 |
0.0118 |
0.965 |
| HMC |
0.3 |
1.531 |
0.142 |
4.499 |
| HMC |
0.5 |
3.007 |
0.00526 |
1.349 |
| HMC |
0.9 |
6.941 |
1.96e-07 |
3.707 |
| HMC |
0.99 |
3.491 |
0.00203 |
2.708 |
| SMC |
0.0 |
7.246 |
6.38e-07 |
17.533 |
| SMC |
0.3 |
5.435 |
2.93e-05 |
16.812 |
| SMC |
0.5 |
10.831 |
1.36e-09 |
49.433 |
| SMC |
0.9 |
8.058 |
1.43e-07 |
29.870 |
| SMC |
0.99 |
9.313 |
1.5e-08 |
30.465 |
| Metro |
0.0 |
7.866 |
1.51e-08 |
3.957 |
| Metro |
0.3 |
8.030 |
1.23e-08 |
4.207 |
| Metro |
0.5 |
6.952 |
8.18e-07 |
7.858 |
| Metro |
0.9 |
6.790 |
1.57e-06 |
15.068 |
| Metro |
0.99 |
5.864 |
1.2e-05 |
55.497 |
| DEMetro_Z |
0.0 |
9.310 |
1.92e-09 |
6.038 |
| DEMetro_Z |
0.3 |
6.934 |
4.96e-07 |
5.219 |
| DEMetro_Z |
0.5 |
6.357 |
2.7e-06 |
6.478 |
| DEMetro_Z |
0.9 |
8.347 |
3.27e-08 |
7.278 |
| DEMetro_Z |
0.99 |
6.269 |
2.46e-06 |
4.937 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
-4.728
|
0.000146
|
-1.057
|
| DEMetro_Z_vs_SMC |
0.3
|
-3.425
|
0.00284
|
-0.766
|
| DEMetro_Z_vs_SMC |
0.5
|
-9.246
|
1.83e-08
|
-2.067
|
| DEMetro_Z_vs_SMC |
0.9
|
-5.986
|
9.25e-06
|
-1.339
|
| DEMetro_Z_vs_SMC |
0.99
|
-7.722
|
2.82e-07
|
-1.727
|
| HMC_vs_Metro |
0.0
|
-5.090
|
6.51e-05
|
-1.138
|
| HMC_vs_Metro |
0.3
|
0.098
|
0.923
|
0.022
|
| HMC_vs_Metro |
0.5
|
-5.776
|
1.45e-05
|
-1.292
|
| HMC_vs_Metro |
0.9
|
-4.853
|
0.00011
|
-1.085
|
| HMC_vs_Metro |
0.99
|
-5.440
|
3e-05
|
-1.217
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.614
|
0.0171
|
-0.585
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.065
|
0.3
|
-0.238
|
| Metro_vs_DEMetro_Z |
0.5
|
0.972
|
0.343
|
0.217
|
| Metro_vs_DEMetro_Z |
0.9
|
3.223
|
0.00448
|
0.721
|
| Metro_vs_DEMetro_Z |
0.99
|
5.152
|
5.67e-05
|
1.152
|
| HMC_vs_SMC |
0.0
|
-6.785
|
1.76e-06
|
-1.517
|
| HMC_vs_SMC |
0.3
|
-2.622
|
0.0168
|
-0.586
|
| HMC_vs_SMC |
0.5
|
-10.552
|
2.2e-09
|
-2.360
|
| HMC_vs_SMC |
0.9
|
-6.713
|
2.04e-06
|
-1.501
|
| HMC_vs_SMC |
0.99
|
-9.259
|
1.79e-08
|
-2.070
|
| Metro_vs_SMC |
0.0
|
-5.424
|
3.11e-05
|
-1.213
|
| Metro_vs_SMC |
0.3
|
-4.254
|
0.000429
|
-0.951
|
| Metro_vs_SMC |
0.5
|
-10.012
|
5.16e-09
|
-2.239
|
| Metro_vs_SMC |
0.9
|
-4.110
|
0.000596
|
-0.919
|
| Metro_vs_SMC |
0.99
|
2.123
|
0.0471
|
0.475
|
| HMC_vs_DEMetro_Z |
0.0
|
-8.958
|
3e-08
|
-2.003
|
| HMC_vs_DEMetro_Z |
0.3
|
-0.252
|
0.803
|
-0.056
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.972
|
9.54e-06
|
-1.335
|
| HMC_vs_DEMetro_Z |
0.9
|
-4.066
|
0.000659
|
-0.909
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.066
|
0.0527
|
-0.462
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.019 |
0.014 |
0.005 |
0.965 |
| HMC |
0.3 |
0.032 |
0.015 |
0.004 |
4.499 |
| HMC |
0.5 |
0.020 |
0.015 |
0.004 |
1.349 |
| HMC |
0.9 |
0.028 |
0.013 |
0.004 |
3.707 |
| HMC |
0.99 |
0.030 |
0.015 |
0.006 |
2.708 |
| SMC |
0.0 |
0.096 |
0.014 |
0.005 |
17.533 |
| SMC |
0.3 |
0.079 |
0.015 |
0.004 |
16.812 |
| SMC |
0.5 |
0.209 |
0.015 |
0.004 |
49.433 |
| SMC |
0.9 |
0.127 |
0.013 |
0.004 |
29.870 |
| SMC |
0.99 |
0.187 |
0.015 |
0.006 |
30.465 |
| Metro |
0.0 |
0.033 |
0.014 |
0.005 |
3.957 |
| Metro |
0.3 |
0.031 |
0.015 |
0.004 |
4.207 |
| Metro |
0.5 |
0.046 |
0.015 |
0.004 |
7.858 |
| Metro |
0.9 |
0.071 |
0.013 |
0.004 |
15.068 |
| Metro |
0.99 |
0.327 |
0.015 |
0.006 |
55.497 |
| DEMetro_Z |
0.0 |
0.043 |
0.014 |
0.005 |
6.038 |
| DEMetro_Z |
0.3 |
0.035 |
0.015 |
0.004 |
5.219 |
| DEMetro_Z |
0.5 |
0.040 |
0.015 |
0.004 |
6.478 |
| DEMetro_Z |
0.9 |
0.041 |
0.013 |
0.004 |
7.278 |
| DEMetro_Z |
0.99 |
0.043 |
0.015 |
0.006 |
4.937 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_high_Multimodality
(Mixture,
correlation,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.646 |
0.000174 |
19.987 |
| HMC |
0.3 |
4.217 |
0.000466 |
33.526 |
| HMC |
0.5 |
5.419 |
3.1e-05 |
24.886 |
| HMC |
0.9 |
4.491 |
0.000248 |
22.867 |
| HMC |
0.99 |
5.252 |
4.52e-05 |
42.278 |
| SMC |
0.0 |
0.346 |
0.732 |
0.134 |
| SMC |
0.3 |
0.993 |
0.328 |
0.380 |
| SMC |
0.5 |
1.316 |
0.196 |
0.403 |
| SMC |
0.9 |
-0.409 |
0.685 |
-0.114 |
| SMC |
0.99 |
1.583 |
0.126 |
0.948 |
| Metro |
0.0 |
3.596 |
0.00191 |
14.990 |
| Metro |
0.3 |
4.145 |
0.000548 |
30.857 |
| Metro |
0.5 |
5.351 |
3.58e-05 |
21.743 |
| Metro |
0.9 |
4.738 |
0.000141 |
21.303 |
| Metro |
0.99 |
5.589 |
2.16e-05 |
42.859 |
| DEMetro_Z |
0.0 |
6.973 |
1.13e-06 |
19.654 |
| DEMetro_Z |
0.3 |
4.964 |
8.55e-05 |
27.936 |
| DEMetro_Z |
0.5 |
5.785 |
1.4e-05 |
31.600 |
| DEMetro_Z |
0.9 |
4.960 |
8.56e-05 |
22.093 |
| DEMetro_Z |
0.99 |
6.161 |
6.35e-06 |
51.519 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
0.081
|
0.936
|
0.018
|
| HMC_vs_DEMetro_Z |
0.3
|
0.516
|
0.612
|
0.115
|
| HMC_vs_DEMetro_Z |
0.5
|
-0.837
|
0.413
|
-0.187
|
| HMC_vs_DEMetro_Z |
0.9
|
0.123
|
0.904
|
0.027
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.832
|
0.416
|
-0.186
|
| Metro_vs_SMC |
0.0
|
3.585
|
0.00197
|
0.802
|
| Metro_vs_SMC |
0.3
|
4.079
|
0.00064
|
0.912
|
| Metro_vs_SMC |
0.5
|
5.286
|
4.21e-05
|
1.182
|
| Metro_vs_SMC |
0.9
|
4.783
|
0.000129
|
1.070
|
| Metro_vs_SMC |
0.99
|
5.452
|
2.93e-05
|
1.219
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.136
|
0.27
|
-0.254
|
| Metro_vs_DEMetro_Z |
0.3
|
0.295
|
0.771
|
0.066
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.279
|
0.216
|
-0.286
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.136
|
0.893
|
-0.030
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.932
|
0.363
|
-0.208
|
| HMC_vs_Metro |
0.0
|
1.787
|
0.0899
|
0.400
|
| HMC_vs_Metro |
0.3
|
0.382
|
0.706
|
0.085
|
| HMC_vs_Metro |
0.5
|
0.620
|
0.543
|
0.139
|
| HMC_vs_Metro |
0.9
|
0.330
|
0.745
|
0.074
|
| HMC_vs_Metro |
0.99
|
-0.053
|
0.958
|
-0.012
|
| HMC_vs_SMC |
0.0
|
4.637
|
0.00018
|
1.037
|
| HMC_vs_SMC |
0.3
|
4.125
|
0.000576
|
0.922
|
| HMC_vs_SMC |
0.5
|
5.383
|
3.41e-05
|
1.204
|
| HMC_vs_SMC |
0.9
|
4.574
|
0.000207
|
1.023
|
| HMC_vs_SMC |
0.99
|
5.221
|
4.86e-05
|
1.168
|
| DEMetro_Z_vs_SMC |
0.0
|
6.848
|
1.55e-06
|
1.531
|
| DEMetro_Z_vs_SMC |
0.3
|
4.842
|
0.000113
|
1.083
|
| DEMetro_Z_vs_SMC |
0.5
|
5.747
|
1.54e-05
|
1.285
|
| DEMetro_Z_vs_SMC |
0.9
|
4.985
|
8.22e-05
|
1.115
|
| DEMetro_Z_vs_SMC |
0.99
|
6.271
|
5.07e-06
|
1.402
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.308 |
0.089 |
0.061 |
19.987 |
| HMC |
0.3 |
1.750 |
0.074 |
0.050 |
33.526 |
| HMC |
0.5 |
1.621 |
0.061 |
0.063 |
24.886 |
| HMC |
0.9 |
1.759 |
0.094 |
0.073 |
22.867 |
| HMC |
0.99 |
1.731 |
0.063 |
0.039 |
42.278 |
| SMC |
0.0 |
0.097 |
0.089 |
0.061 |
0.134 |
| SMC |
0.3 |
0.093 |
0.074 |
0.050 |
0.380 |
| SMC |
0.5 |
0.087 |
0.061 |
0.063 |
0.403 |
| SMC |
0.9 |
0.086 |
0.094 |
0.073 |
-0.114 |
| SMC |
0.99 |
0.100 |
0.063 |
0.039 |
0.948 |
| Metro |
0.0 |
1.003 |
0.089 |
0.061 |
14.990 |
| Metro |
0.3 |
1.616 |
0.074 |
0.050 |
30.857 |
| Metro |
0.5 |
1.424 |
0.061 |
0.063 |
21.743 |
| Metro |
0.9 |
1.645 |
0.094 |
0.073 |
21.303 |
| Metro |
0.99 |
1.754 |
0.063 |
0.039 |
42.859 |
| DEMetro_Z |
0.0 |
1.288 |
0.089 |
0.061 |
19.654 |
| DEMetro_Z |
0.3 |
1.470 |
0.074 |
0.050 |
27.936 |
| DEMetro_Z |
0.5 |
2.041 |
0.061 |
0.063 |
31.600 |
| DEMetro_Z |
0.9 |
1.702 |
0.094 |
0.073 |
22.093 |
| DEMetro_Z |
0.99 |
2.096 |
0.063 |
0.039 |
51.519 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.759 |
0.000135 |
29.361 |
| HMC |
0.3 |
3.319 |
0.0036 |
62.876 |
| HMC |
0.5 |
3.960 |
0.000839 |
61.399 |
| HMC |
0.9 |
3.459 |
0.00263 |
76.998 |
| HMC |
0.99 |
3.645 |
0.00172 |
57.387 |
| SMC |
0.0 |
-0.916 |
0.366 |
-0.257 |
| SMC |
0.3 |
-0.246 |
0.807 |
-0.079 |
| SMC |
0.5 |
0.424 |
0.674 |
0.168 |
| SMC |
0.9 |
1.810 |
0.0801 |
0.805 |
| SMC |
0.99 |
0.559 |
0.58 |
0.202 |
| Metro |
0.0 |
3.741 |
0.00138 |
22.257 |
| Metro |
0.3 |
3.202 |
0.00469 |
54.169 |
| Metro |
0.5 |
5.637 |
1.94e-05 |
47.506 |
| Metro |
0.9 |
3.700 |
0.00152 |
70.026 |
| Metro |
0.99 |
4.160 |
0.000531 |
64.135 |
| DEMetro_Z |
0.0 |
4.409 |
0.000299 |
22.883 |
| DEMetro_Z |
0.3 |
2.949 |
0.00824 |
36.970 |
| DEMetro_Z |
0.5 |
4.167 |
0.000523 |
94.488 |
| DEMetro_Z |
0.9 |
3.501 |
0.00239 |
66.823 |
| DEMetro_Z |
0.99 |
4.212 |
0.000471 |
74.390 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
4.854
|
0.00011
|
1.085
|
| HMC_vs_SMC |
0.3
|
3.322
|
0.00358
|
0.743
|
| HMC_vs_SMC |
0.5
|
3.928
|
0.000903
|
0.878
|
| HMC_vs_SMC |
0.9
|
3.415
|
0.0029
|
0.764
|
| HMC_vs_SMC |
0.99
|
3.639
|
0.00174
|
0.814
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.093
|
0.927
|
-0.021
|
| Metro_vs_DEMetro_Z |
0.3
|
0.728
|
0.476
|
0.163
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.758
|
0.0948
|
-0.393
|
| Metro_vs_DEMetro_Z |
0.9
|
0.116
|
0.909
|
0.026
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.812
|
0.427
|
-0.182
|
| HMC_vs_Metro |
0.0
|
1.649
|
0.116
|
0.369
|
| HMC_vs_Metro |
0.3
|
0.422
|
0.678
|
0.094
|
| HMC_vs_Metro |
0.5
|
0.884
|
0.388
|
0.198
|
| HMC_vs_Metro |
0.9
|
0.461
|
0.65
|
0.103
|
| HMC_vs_Metro |
0.99
|
-0.304
|
0.764
|
-0.068
|
| HMC_vs_DEMetro_Z |
0.0
|
0.958
|
0.35
|
0.214
|
| HMC_vs_DEMetro_Z |
0.3
|
1.026
|
0.318
|
0.229
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.074
|
0.296
|
-0.240
|
| HMC_vs_DEMetro_Z |
0.9
|
0.340
|
0.737
|
0.076
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.709
|
0.487
|
-0.159
|
| Metro_vs_SMC |
0.0
|
3.839
|
0.00111
|
0.858
|
| Metro_vs_SMC |
0.3
|
3.211
|
0.0046
|
0.718
|
| Metro_vs_SMC |
0.5
|
5.615
|
2.05e-05
|
1.256
|
| Metro_vs_SMC |
0.9
|
3.643
|
0.00173
|
0.815
|
| Metro_vs_SMC |
0.99
|
4.165
|
0.000526
|
0.931
|
| DEMetro_Z_vs_SMC |
0.0
|
4.538
|
0.000225
|
1.015
|
| DEMetro_Z_vs_SMC |
0.3
|
2.973
|
0.00782
|
0.665
|
| DEMetro_Z_vs_SMC |
0.5
|
4.142
|
0.000554
|
0.926
|
| DEMetro_Z_vs_SMC |
0.9
|
3.458
|
0.00264
|
0.773
|
| DEMetro_Z_vs_SMC |
0.99
|
4.222
|
0.000462
|
0.944
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.142 |
0.191 |
0.135 |
29.361 |
| HMC |
0.3 |
8.653 |
0.190 |
0.135 |
62.876 |
| HMC |
0.5 |
6.014 |
0.153 |
0.095 |
61.399 |
| HMC |
0.9 |
7.900 |
0.150 |
0.101 |
76.998 |
| HMC |
0.99 |
7.049 |
0.170 |
0.120 |
57.387 |
| SMC |
0.0 |
0.156 |
0.191 |
0.135 |
-0.257 |
| SMC |
0.3 |
0.180 |
0.190 |
0.135 |
-0.079 |
| SMC |
0.5 |
0.169 |
0.153 |
0.095 |
0.168 |
| SMC |
0.9 |
0.231 |
0.150 |
0.101 |
0.805 |
| SMC |
0.99 |
0.194 |
0.170 |
0.120 |
0.202 |
| Metro |
0.0 |
3.186 |
0.191 |
0.135 |
22.257 |
| Metro |
0.3 |
7.481 |
0.190 |
0.135 |
54.169 |
| Metro |
0.5 |
4.688 |
0.153 |
0.095 |
47.506 |
| Metro |
0.9 |
7.198 |
0.150 |
0.101 |
70.026 |
| Metro |
0.99 |
7.858 |
0.170 |
0.120 |
64.135 |
| DEMetro_Z |
0.0 |
3.270 |
0.191 |
0.135 |
22.883 |
| DEMetro_Z |
0.3 |
5.166 |
0.190 |
0.135 |
36.970 |
| DEMetro_Z |
0.5 |
9.173 |
0.153 |
0.095 |
94.488 |
| DEMetro_Z |
0.9 |
6.876 |
0.150 |
0.101 |
66.823 |
| DEMetro_Z |
0.99 |
9.088 |
0.170 |
0.120 |
74.390 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.663 |
0.000168 |
22.529 |
| HMC |
0.3 |
4.083 |
0.000632 |
35.588 |
| HMC |
0.5 |
5.425 |
3.06e-05 |
26.491 |
| HMC |
0.9 |
4.457 |
0.000268 |
25.976 |
| HMC |
0.99 |
5.332 |
3.79e-05 |
46.194 |
| SMC |
0.0 |
0.509 |
0.614 |
0.202 |
| SMC |
0.3 |
0.857 |
0.397 |
0.311 |
| SMC |
0.5 |
1.105 |
0.276 |
0.333 |
| SMC |
0.9 |
-0.362 |
0.719 |
-0.106 |
| SMC |
0.99 |
1.519 |
0.142 |
0.940 |
| Metro |
0.0 |
3.644 |
0.00172 |
15.995 |
| Metro |
0.3 |
4.175 |
0.000512 |
33.030 |
| Metro |
0.5 |
5.408 |
3.17e-05 |
24.409 |
| Metro |
0.9 |
4.863 |
0.000107 |
23.833 |
| Metro |
0.99 |
5.795 |
1.38e-05 |
48.433 |
| DEMetro_Z |
0.0 |
6.867 |
1.42e-06 |
21.553 |
| DEMetro_Z |
0.3 |
4.843 |
0.000112 |
29.654 |
| DEMetro_Z |
0.5 |
5.898 |
1.1e-05 |
34.601 |
| DEMetro_Z |
0.9 |
4.970 |
8.41e-05 |
24.282 |
| DEMetro_Z |
0.99 |
6.047 |
8.09e-06 |
54.708 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-1.273
|
0.218
|
-0.285
|
| Metro_vs_DEMetro_Z |
0.3
|
0.316
|
0.756
|
0.071
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.201
|
0.244
|
-0.269
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.069
|
0.945
|
-0.015
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.665
|
0.514
|
-0.149
|
| DEMetro_Z_vs_SMC |
0.0
|
6.749
|
1.9e-06
|
1.509
|
| DEMetro_Z_vs_SMC |
0.3
|
4.759
|
0.000137
|
1.064
|
| DEMetro_Z_vs_SMC |
0.5
|
5.862
|
1.2e-05
|
1.311
|
| DEMetro_Z_vs_SMC |
0.9
|
4.989
|
8.15e-05
|
1.116
|
| DEMetro_Z_vs_SMC |
0.99
|
6.176
|
6.2e-06
|
1.381
|
| HMC_vs_DEMetro_Z |
0.0
|
0.211
|
0.835
|
0.047
|
| HMC_vs_DEMetro_Z |
0.3
|
0.497
|
0.625
|
0.111
|
| HMC_vs_DEMetro_Z |
0.5
|
-0.935
|
0.361
|
-0.209
|
| HMC_vs_DEMetro_Z |
0.9
|
0.242
|
0.812
|
0.054
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.729
|
0.475
|
-0.163
|
| HMC_vs_Metro |
0.0
|
1.947
|
0.0664
|
0.435
|
| HMC_vs_Metro |
0.3
|
0.323
|
0.75
|
0.072
|
| HMC_vs_Metro |
0.5
|
0.371
|
0.715
|
0.083
|
| HMC_vs_Metro |
0.9
|
0.396
|
0.696
|
0.089
|
| HMC_vs_Metro |
0.99
|
-0.184
|
0.856
|
-0.041
|
| HMC_vs_SMC |
0.0
|
4.653
|
0.000173
|
1.040
|
| HMC_vs_SMC |
0.3
|
4.011
|
0.000747
|
0.897
|
| HMC_vs_SMC |
0.5
|
5.405
|
3.24e-05
|
1.209
|
| HMC_vs_SMC |
0.9
|
4.512
|
0.000238
|
1.009
|
| HMC_vs_SMC |
0.99
|
5.330
|
3.82e-05
|
1.192
|
| Metro_vs_SMC |
0.0
|
3.635
|
0.00176
|
0.813
|
| Metro_vs_SMC |
0.3
|
4.124
|
0.000577
|
0.922
|
| Metro_vs_SMC |
0.5
|
5.373
|
3.48e-05
|
1.201
|
| Metro_vs_SMC |
0.9
|
4.874
|
0.000105
|
1.090
|
| Metro_vs_SMC |
0.99
|
5.690
|
1.74e-05
|
1.272
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.196 |
0.096 |
0.049 |
22.529 |
| HMC |
0.3 |
1.585 |
0.087 |
0.042 |
35.588 |
| HMC |
0.5 |
1.421 |
0.078 |
0.051 |
26.491 |
| HMC |
0.9 |
1.600 |
0.103 |
0.058 |
25.976 |
| HMC |
0.99 |
1.590 |
0.077 |
0.033 |
46.194 |
| SMC |
0.0 |
0.106 |
0.096 |
0.049 |
0.202 |
| SMC |
0.3 |
0.100 |
0.087 |
0.042 |
0.311 |
| SMC |
0.5 |
0.095 |
0.078 |
0.051 |
0.333 |
| SMC |
0.9 |
0.096 |
0.103 |
0.058 |
-0.106 |
| SMC |
0.99 |
0.107 |
0.077 |
0.033 |
0.940 |
| Metro |
0.0 |
0.877 |
0.096 |
0.049 |
15.995 |
| Metro |
0.3 |
1.477 |
0.087 |
0.042 |
33.030 |
| Metro |
0.5 |
1.316 |
0.078 |
0.051 |
24.409 |
| Metro |
0.9 |
1.476 |
0.103 |
0.058 |
23.833 |
| Metro |
0.99 |
1.664 |
0.077 |
0.033 |
48.433 |
| DEMetro_Z |
0.0 |
1.148 |
0.096 |
0.049 |
21.553 |
| DEMetro_Z |
0.3 |
1.335 |
0.087 |
0.042 |
29.654 |
| DEMetro_Z |
0.5 |
1.833 |
0.078 |
0.051 |
34.601 |
| DEMetro_Z |
0.9 |
1.502 |
0.103 |
0.058 |
24.282 |
| DEMetro_Z |
0.99 |
1.869 |
0.077 |
0.033 |
54.708 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.672 |
0.000164 |
24.183 |
| HMC |
0.3 |
4.302 |
0.000384 |
37.951 |
| HMC |
0.5 |
5.487 |
2.68e-05 |
29.001 |
| HMC |
0.9 |
4.677 |
0.000163 |
24.294 |
| HMC |
0.99 |
5.412 |
3.18e-05 |
45.826 |
| SMC |
0.0 |
0.305 |
0.762 |
0.121 |
| SMC |
0.3 |
0.953 |
0.347 |
0.364 |
| SMC |
0.5 |
1.265 |
0.214 |
0.412 |
| SMC |
0.9 |
-0.345 |
0.732 |
-0.096 |
| SMC |
0.99 |
1.491 |
0.149 |
0.925 |
| Metro |
0.0 |
3.651 |
0.00169 |
18.145 |
| Metro |
0.3 |
4.229 |
0.000453 |
36.256 |
| Metro |
0.5 |
5.371 |
3.44e-05 |
25.596 |
| Metro |
0.9 |
4.825 |
0.000116 |
22.965 |
| Metro |
0.99 |
5.783 |
1.42e-05 |
48.534 |
| DEMetro_Z |
0.0 |
7.120 |
8.58e-07 |
23.781 |
| DEMetro_Z |
0.3 |
5.181 |
5.27e-05 |
32.525 |
| DEMetro_Z |
0.5 |
5.905 |
1.09e-05 |
36.366 |
| DEMetro_Z |
0.9 |
5.064 |
6.8e-05 |
23.395 |
| DEMetro_Z |
0.99 |
6.348 |
4.3e-06 |
54.939 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
7.047
|
1.05e-06
|
1.576
|
| DEMetro_Z_vs_SMC |
0.3
|
5.091
|
6.49e-05
|
1.138
|
| DEMetro_Z_vs_SMC |
0.5
|
5.854
|
1.23e-05
|
1.309
|
| DEMetro_Z_vs_SMC |
0.9
|
5.103
|
6.32e-05
|
1.141
|
| DEMetro_Z_vs_SMC |
0.99
|
6.466
|
3.39e-06
|
1.446
|
| HMC_vs_Metro |
0.0
|
1.826
|
0.0836
|
0.408
|
| HMC_vs_Metro |
0.3
|
0.222
|
0.827
|
0.050
|
| HMC_vs_Metro |
0.5
|
0.575
|
0.572
|
0.129
|
| HMC_vs_Metro |
0.9
|
0.262
|
0.796
|
0.059
|
| HMC_vs_Metro |
0.99
|
-0.225
|
0.824
|
-0.050
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.164
|
0.259
|
-0.260
|
| Metro_vs_DEMetro_Z |
0.3
|
0.334
|
0.742
|
0.075
|
| Metro_vs_DEMetro_Z |
0.5
|
-1.224
|
0.236
|
-0.274
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.071
|
0.944
|
-0.016
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.668
|
0.512
|
-0.149
|
| HMC_vs_SMC |
0.0
|
4.679
|
0.000163
|
1.046
|
| HMC_vs_SMC |
0.3
|
4.228
|
0.000456
|
0.945
|
| HMC_vs_SMC |
0.5
|
5.460
|
2.87e-05
|
1.221
|
| HMC_vs_SMC |
0.9
|
4.751
|
0.000139
|
1.062
|
| HMC_vs_SMC |
0.99
|
5.421
|
3.13e-05
|
1.212
|
| Metro_vs_SMC |
0.0
|
3.655
|
0.00169
|
0.817
|
| Metro_vs_SMC |
0.3
|
4.189
|
0.000498
|
0.937
|
| Metro_vs_SMC |
0.5
|
5.305
|
4.04e-05
|
1.186
|
| Metro_vs_SMC |
0.9
|
4.840
|
0.000114
|
1.082
|
| Metro_vs_SMC |
0.99
|
5.666
|
1.84e-05
|
1.267
|
| HMC_vs_DEMetro_Z |
0.0
|
0.083
|
0.935
|
0.019
|
| HMC_vs_DEMetro_Z |
0.3
|
0.452
|
0.656
|
0.101
|
| HMC_vs_DEMetro_Z |
0.5
|
-0.809
|
0.428
|
-0.181
|
| HMC_vs_DEMetro_Z |
0.9
|
0.141
|
0.889
|
0.032
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.797
|
0.436
|
-0.178
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.187 |
0.012 |
0.007 |
24.183 |
| HMC |
0.3 |
0.239 |
0.011 |
0.006 |
37.951 |
| HMC |
0.5 |
0.227 |
0.009 |
0.008 |
29.001 |
| HMC |
0.9 |
0.250 |
0.013 |
0.010 |
24.294 |
| HMC |
0.99 |
0.247 |
0.009 |
0.005 |
45.826 |
| SMC |
0.0 |
0.013 |
0.012 |
0.007 |
0.121 |
| SMC |
0.3 |
0.013 |
0.011 |
0.006 |
0.364 |
| SMC |
0.5 |
0.012 |
0.009 |
0.008 |
0.412 |
| SMC |
0.9 |
0.012 |
0.013 |
0.010 |
-0.096 |
| SMC |
0.99 |
0.013 |
0.009 |
0.005 |
0.925 |
| Metro |
0.0 |
0.144 |
0.012 |
0.007 |
18.145 |
| Metro |
0.3 |
0.229 |
0.011 |
0.006 |
36.256 |
| Metro |
0.5 |
0.202 |
0.009 |
0.008 |
25.596 |
| Metro |
0.9 |
0.237 |
0.013 |
0.010 |
22.965 |
| Metro |
0.99 |
0.261 |
0.009 |
0.005 |
48.534 |
| DEMetro_Z |
0.0 |
0.184 |
0.012 |
0.007 |
23.781 |
| DEMetro_Z |
0.3 |
0.207 |
0.011 |
0.006 |
32.525 |
| DEMetro_Z |
0.5 |
0.283 |
0.009 |
0.008 |
36.366 |
| DEMetro_Z |
0.9 |
0.241 |
0.013 |
0.010 |
23.395 |
| DEMetro_Z |
0.99 |
0.295 |
0.009 |
0.005 |
54.939 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
220.345 |
6.06e-60 |
74.195 |
| HMC |
0.3 |
203.371 |
2.67e-49 |
90.695 |
| HMC |
0.5 |
235.973 |
1.29e-61 |
72.628 |
| HMC |
0.9 |
195.028 |
1.24e-58 |
61.681 |
| HMC |
0.99 |
214.236 |
8.12e-45 |
114.222 |
| SMC |
0.0 |
-0.031 |
0.976 |
-0.010 |
| SMC |
0.3 |
1.597 |
0.119 |
0.562 |
| SMC |
0.5 |
0.793 |
0.433 |
0.247 |
| SMC |
0.9 |
-0.078 |
0.939 |
-0.027 |
| SMC |
0.99 |
2.219 |
0.0341 |
0.995 |
| Metro |
0.0 |
45.607 |
1.68e-21 |
72.561 |
| Metro |
0.3 |
191.990 |
8.41e-47 |
90.527 |
| Metro |
0.5 |
229.596 |
2.58e-61 |
73.101 |
| Metro |
0.9 |
155.196 |
2.33e-49 |
61.829 |
| Metro |
0.99 |
59.923 |
1.37e-23 |
116.636 |
| DEMetro_Z |
0.0 |
11.179 |
8.2e-10 |
63.677 |
| DEMetro_Z |
0.3 |
9.459 |
1.26e-08 |
73.661 |
| DEMetro_Z |
0.5 |
9.500 |
1.17e-08 |
59.057 |
| DEMetro_Z |
0.9 |
178.034 |
1.04e-55 |
61.993 |
| DEMetro_Z |
0.99 |
224.143 |
4.06e-46 |
115.899 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
1.855
|
0.0792
|
0.415
|
| HMC_vs_DEMetro_Z |
0.3
|
2.160
|
0.0438
|
0.483
|
| HMC_vs_DEMetro_Z |
0.5
|
2.187
|
0.0414
|
0.489
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.315
|
0.204
|
-0.294
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.155
|
0.0442
|
-0.482
|
| Metro_vs_SMC |
0.0
|
46.692
|
4.52e-21
|
10.441
|
| Metro_vs_SMC |
0.3
|
208.613
|
2.17e-33
|
46.647
|
| Metro_vs_SMC |
0.5
|
281.458
|
7.33e-36
|
62.936
|
| Metro_vs_SMC |
0.9
|
130.986
|
1.49e-29
|
29.289
|
| Metro_vs_SMC |
0.99
|
61.530
|
2.47e-23
|
13.758
|
| Metro_vs_DEMetro_Z |
0.0
|
1.474
|
0.157
|
0.329
|
| Metro_vs_DEMetro_Z |
0.3
|
2.141
|
0.0455
|
0.479
|
| Metro_vs_DEMetro_Z |
0.5
|
2.265
|
0.0354
|
0.506
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.459
|
0.651
|
-0.103
|
| Metro_vs_DEMetro_Z |
0.99
|
0.396
|
0.697
|
0.089
|
| HMC_vs_Metro |
0.0
|
1.032
|
0.315
|
0.231
|
| HMC_vs_Metro |
0.3
|
0.552
|
0.587
|
0.124
|
| HMC_vs_Metro |
0.5
|
-1.770
|
0.0928
|
-0.396
|
| HMC_vs_Metro |
0.9
|
-0.443
|
0.663
|
-0.099
|
| HMC_vs_Metro |
0.99
|
-1.078
|
0.294
|
-0.241
|
| HMC_vs_SMC |
0.0
|
235.552
|
2.16e-34
|
52.671
|
| HMC_vs_SMC |
0.3
|
218.223
|
9.21e-34
|
48.796
|
| HMC_vs_SMC |
0.5
|
214.995
|
1.22e-33
|
48.074
|
| HMC_vs_SMC |
0.9
|
150.083
|
1.13e-30
|
33.560
|
| HMC_vs_SMC |
0.99
|
145.562
|
2.01e-30
|
32.549
|
| DEMetro_Z_vs_SMC |
0.0
|
10.961
|
1.18e-09
|
2.451
|
| DEMetro_Z_vs_SMC |
0.3
|
9.364
|
1.5e-08
|
2.094
|
| DEMetro_Z_vs_SMC |
0.5
|
9.477
|
1.24e-08
|
2.119
|
| DEMetro_Z_vs_SMC |
0.9
|
130.787
|
1.53e-29
|
29.245
|
| DEMetro_Z_vs_SMC |
0.99
|
316.126
|
8.07e-37
|
70.688
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.616 |
0.089 |
0.061 |
74.195 |
| HMC |
0.3 |
4.606 |
0.074 |
0.050 |
90.695 |
| HMC |
0.5 |
4.612 |
0.061 |
0.063 |
72.628 |
| HMC |
0.9 |
4.584 |
0.094 |
0.073 |
61.681 |
| HMC |
0.99 |
4.571 |
0.063 |
0.039 |
114.222 |
| SMC |
0.0 |
0.088 |
0.089 |
0.061 |
-0.010 |
| SMC |
0.3 |
0.102 |
0.074 |
0.050 |
0.562 |
| SMC |
0.5 |
0.077 |
0.061 |
0.063 |
0.247 |
| SMC |
0.9 |
0.092 |
0.094 |
0.073 |
-0.027 |
| SMC |
0.99 |
0.102 |
0.063 |
0.039 |
0.995 |
| Metro |
0.0 |
4.516 |
0.089 |
0.061 |
72.561 |
| Metro |
0.3 |
4.598 |
0.074 |
0.050 |
90.527 |
| Metro |
0.5 |
4.642 |
0.061 |
0.063 |
73.101 |
| Metro |
0.9 |
4.595 |
0.094 |
0.073 |
61.829 |
| Metro |
0.99 |
4.666 |
0.063 |
0.039 |
116.636 |
| DEMetro_Z |
0.0 |
3.974 |
0.089 |
0.061 |
63.677 |
| DEMetro_Z |
0.3 |
3.755 |
0.074 |
0.050 |
73.661 |
| DEMetro_Z |
0.5 |
3.762 |
0.061 |
0.063 |
59.057 |
| DEMetro_Z |
0.9 |
4.607 |
0.094 |
0.073 |
61.993 |
| DEMetro_Z |
0.99 |
4.637 |
0.063 |
0.039 |
115.899 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
757.030 |
8.28e-79 |
220.550 |
| HMC |
0.3 |
539.147 |
3.52e-66 |
220.442 |
| HMC |
0.5 |
710.928 |
1.08e-66 |
311.457 |
| HMC |
0.9 |
667.013 |
2.18e-65 |
295.034 |
| HMC |
0.99 |
608.754 |
4.09e-68 |
247.849 |
| SMC |
0.0 |
-1.771 |
0.0855 |
-0.486 |
| SMC |
0.3 |
0.098 |
0.922 |
0.032 |
| SMC |
0.5 |
1.884 |
0.0686 |
0.788 |
| SMC |
0.9 |
0.513 |
0.611 |
0.159 |
| SMC |
0.99 |
0.738 |
0.465 |
0.260 |
| Metro |
0.0 |
28.731 |
3.85e-17 |
213.058 |
| Metro |
0.3 |
552.862 |
9.51e-68 |
220.456 |
| Metro |
0.5 |
719.475 |
1.98e-67 |
311.443 |
| Metro |
0.9 |
662.763 |
5.93e-65 |
295.400 |
| Metro |
0.99 |
348.360 |
1.61e-44 |
247.662 |
| DEMetro_Z |
0.0 |
10.487 |
2.42e-09 |
187.919 |
| DEMetro_Z |
0.3 |
8.776 |
4.12e-08 |
176.381 |
| DEMetro_Z |
0.5 |
8.769 |
4.17e-08 |
249.598 |
| DEMetro_Z |
0.9 |
651.591 |
5.71e-64 |
295.361 |
| DEMetro_Z |
0.99 |
590.385 |
3.22e-66 |
247.712 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
793.745
|
2.05e-44
|
177.487
|
| HMC_vs_SMC |
0.3
|
537.846
|
3.33e-41
|
120.266
|
| HMC_vs_SMC |
0.5
|
574.521
|
9.51e-42
|
128.467
|
| HMC_vs_SMC |
0.9
|
717.529
|
1.39e-43
|
160.444
|
| HMC_vs_SMC |
0.99
|
451.921
|
9.09e-40
|
101.053
|
| Metro_vs_DEMetro_Z |
0.0
|
1.254
|
0.225
|
0.280
|
| Metro_vs_DEMetro_Z |
0.3
|
2.179
|
0.0421
|
0.487
|
| Metro_vs_DEMetro_Z |
0.5
|
2.175
|
0.0425
|
0.486
|
| Metro_vs_DEMetro_Z |
0.9
|
0.277
|
0.785
|
0.062
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.084
|
0.934
|
-0.019
|
| HMC_vs_Metro |
0.0
|
1.003
|
0.328
|
0.224
|
| HMC_vs_Metro |
0.3
|
-0.198
|
0.845
|
-0.044
|
| HMC_vs_Metro |
0.5
|
0.116
|
0.909
|
0.026
|
| HMC_vs_Metro |
0.9
|
-2.618
|
0.0169
|
-0.585
|
| HMC_vs_Metro |
0.99
|
0.325
|
0.749
|
0.073
|
| HMC_vs_DEMetro_Z |
0.0
|
1.823
|
0.0841
|
0.408
|
| HMC_vs_DEMetro_Z |
0.3
|
2.176
|
0.0424
|
0.486
|
| HMC_vs_DEMetro_Z |
0.5
|
2.178
|
0.0422
|
0.487
|
| HMC_vs_DEMetro_Z |
0.9
|
-3.950
|
0.00086
|
-0.883
|
| HMC_vs_DEMetro_Z |
0.99
|
1.299
|
0.209
|
0.291
|
| Metro_vs_SMC |
0.0
|
28.703
|
4.12e-17
|
6.418
|
| Metro_vs_SMC |
0.3
|
565.285
|
1.29e-41
|
126.402
|
| Metro_vs_SMC |
0.5
|
581.126
|
7.65e-42
|
129.944
|
| Metro_vs_SMC |
0.9
|
708.188
|
1.79e-43
|
158.356
|
| Metro_vs_SMC |
0.99
|
300.632
|
2.1e-36
|
67.223
|
| DEMetro_Z_vs_SMC |
0.0
|
10.526
|
2.29e-09
|
2.354
|
| DEMetro_Z_vs_SMC |
0.3
|
8.755
|
4.28e-08
|
1.958
|
| DEMetro_Z_vs_SMC |
0.5
|
8.732
|
4.46e-08
|
1.953
|
| DEMetro_Z_vs_SMC |
0.9
|
683.875
|
3.47e-43
|
152.919
|
| DEMetro_Z_vs_SMC |
0.99
|
444.638
|
1.24e-39
|
99.424
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
29.872 |
0.191 |
0.135 |
220.550 |
| HMC |
0.3 |
29.862 |
0.190 |
0.135 |
220.442 |
| HMC |
0.5 |
29.886 |
0.153 |
0.095 |
311.457 |
| HMC |
0.9 |
29.845 |
0.150 |
0.101 |
295.034 |
| HMC |
0.99 |
29.883 |
0.170 |
0.120 |
247.849 |
| SMC |
0.0 |
0.125 |
0.191 |
0.135 |
-0.486 |
| SMC |
0.3 |
0.195 |
0.190 |
0.135 |
0.032 |
| SMC |
0.5 |
0.228 |
0.153 |
0.095 |
0.788 |
| SMC |
0.9 |
0.166 |
0.150 |
0.101 |
0.159 |
| SMC |
0.99 |
0.201 |
0.170 |
0.120 |
0.260 |
| Metro |
0.0 |
28.864 |
0.191 |
0.135 |
213.058 |
| Metro |
0.3 |
29.864 |
0.190 |
0.135 |
220.456 |
| Metro |
0.5 |
29.884 |
0.153 |
0.095 |
311.443 |
| Metro |
0.9 |
29.882 |
0.150 |
0.101 |
295.400 |
| Metro |
0.99 |
29.861 |
0.170 |
0.120 |
247.662 |
| DEMetro_Z |
0.0 |
25.480 |
0.191 |
0.135 |
187.919 |
| DEMetro_Z |
0.3 |
23.932 |
0.190 |
0.135 |
176.381 |
| DEMetro_Z |
0.5 |
23.980 |
0.153 |
0.095 |
249.598 |
| DEMetro_Z |
0.9 |
29.878 |
0.150 |
0.101 |
295.361 |
| DEMetro_Z |
0.99 |
29.867 |
0.170 |
0.120 |
247.712 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
59.935 |
5.15e-24 |
85.146 |
| HMC |
0.3 |
48.313 |
9.23e-22 |
95.823 |
| HMC |
0.5 |
73.028 |
1.99e-26 |
79.556 |
| HMC |
0.9 |
74.672 |
2.44e-27 |
68.688 |
| HMC |
0.99 |
83.269 |
8.31e-27 |
121.065 |
| SMC |
0.0 |
0.178 |
0.86 |
0.063 |
| SMC |
0.3 |
1.142 |
0.261 |
0.381 |
| SMC |
0.5 |
0.734 |
0.467 |
0.239 |
| SMC |
0.9 |
-0.089 |
0.93 |
-0.034 |
| SMC |
0.99 |
2.011 |
0.0534 |
0.915 |
| Metro |
0.0 |
34.403 |
7.98e-19 |
80.247 |
| Metro |
0.3 |
78.112 |
1.22e-26 |
96.305 |
| Metro |
0.5 |
56.757 |
1.41e-23 |
79.191 |
| Metro |
0.9 |
56.063 |
1.22e-23 |
71.856 |
| Metro |
0.99 |
36.740 |
3.15e-19 |
128.084 |
| DEMetro_Z |
0.0 |
10.970 |
1.13e-09 |
72.489 |
| DEMetro_Z |
0.3 |
9.459 |
1.26e-08 |
78.539 |
| DEMetro_Z |
0.5 |
9.419 |
1.34e-08 |
67.401 |
| DEMetro_Z |
0.9 |
53.599 |
3.27e-23 |
69.923 |
| DEMetro_Z |
0.99 |
62.861 |
5.35e-24 |
121.756 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
1.066
|
0.3
|
0.238
|
| Metro_vs_DEMetro_Z |
0.3
|
2.162
|
0.0436
|
0.483
|
| Metro_vs_DEMetro_Z |
0.5
|
1.642
|
0.117
|
0.367
|
| Metro_vs_DEMetro_Z |
0.9
|
1.110
|
0.281
|
0.248
|
| Metro_vs_DEMetro_Z |
0.99
|
1.700
|
0.106
|
0.380
|
| DEMetro_Z_vs_SMC |
0.0
|
10.756
|
1.61e-09
|
2.405
|
| DEMetro_Z_vs_SMC |
0.3
|
9.379
|
1.46e-08
|
2.097
|
| DEMetro_Z_vs_SMC |
0.5
|
9.415
|
1.38e-08
|
2.105
|
| DEMetro_Z_vs_SMC |
0.9
|
54.579
|
2.38e-22
|
12.204
|
| DEMetro_Z_vs_SMC |
0.99
|
64.759
|
9.39e-24
|
14.480
|
| HMC_vs_DEMetro_Z |
0.0
|
1.900
|
0.0727
|
0.425
|
| HMC_vs_DEMetro_Z |
0.3
|
1.785
|
0.0902
|
0.399
|
| HMC_vs_DEMetro_Z |
0.5
|
1.649
|
0.115
|
0.369
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.702
|
0.491
|
-0.157
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.319
|
0.753
|
-0.071
|
| HMC_vs_Metro |
0.0
|
1.537
|
0.141
|
0.344
|
| HMC_vs_Metro |
0.3
|
-0.191
|
0.85
|
-0.043
|
| HMC_vs_Metro |
0.5
|
0.202
|
0.842
|
0.045
|
| HMC_vs_Metro |
0.9
|
-2.175
|
0.0424
|
-0.486
|
| HMC_vs_Metro |
0.99
|
-1.956
|
0.0654
|
-0.437
|
| HMC_vs_SMC |
0.0
|
53.907
|
3.01e-22
|
12.054
|
| HMC_vs_SMC |
0.3
|
49.565
|
1.47e-21
|
11.083
|
| HMC_vs_SMC |
0.5
|
69.538
|
2.44e-24
|
15.549
|
| HMC_vs_SMC |
0.9
|
69.193
|
2.68e-24
|
15.472
|
| HMC_vs_SMC |
0.99
|
76.022
|
4.51e-25
|
16.999
|
| Metro_vs_SMC |
0.0
|
34.407
|
1.4e-18
|
7.694
|
| Metro_vs_SMC |
0.3
|
71.041
|
1.63e-24
|
15.885
|
| Metro_vs_SMC |
0.5
|
54.649
|
2.32e-22
|
12.220
|
| Metro_vs_SMC |
0.9
|
53.717
|
3.21e-22
|
12.012
|
| Metro_vs_SMC |
0.99
|
38.778
|
1.49e-19
|
8.671
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.254 |
0.096 |
0.049 |
85.146 |
| HMC |
0.3 |
4.119 |
0.087 |
0.042 |
95.823 |
| HMC |
0.5 |
4.113 |
0.078 |
0.051 |
79.556 |
| HMC |
0.9 |
4.061 |
0.103 |
0.058 |
68.688 |
| HMC |
0.99 |
4.044 |
0.077 |
0.033 |
121.065 |
| SMC |
0.0 |
0.099 |
0.096 |
0.049 |
0.063 |
| SMC |
0.3 |
0.103 |
0.087 |
0.042 |
0.381 |
| SMC |
0.5 |
0.090 |
0.078 |
0.051 |
0.239 |
| SMC |
0.9 |
0.101 |
0.103 |
0.058 |
-0.034 |
| SMC |
0.99 |
0.107 |
0.077 |
0.033 |
0.915 |
| Metro |
0.0 |
4.015 |
0.096 |
0.049 |
80.247 |
| Metro |
0.3 |
4.140 |
0.087 |
0.042 |
96.305 |
| Metro |
0.5 |
4.095 |
0.078 |
0.051 |
79.191 |
| Metro |
0.9 |
4.243 |
0.103 |
0.058 |
71.856 |
| Metro |
0.99 |
4.274 |
0.077 |
0.033 |
128.084 |
| DEMetro_Z |
0.0 |
3.636 |
0.096 |
0.049 |
72.489 |
| DEMetro_Z |
0.3 |
3.392 |
0.087 |
0.042 |
78.539 |
| DEMetro_Z |
0.5 |
3.497 |
0.078 |
0.051 |
67.401 |
| DEMetro_Z |
0.9 |
4.132 |
0.103 |
0.058 |
69.923 |
| DEMetro_Z |
0.99 |
4.067 |
0.077 |
0.033 |
121.756 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
148.640 |
3.46e-39 |
84.937 |
| HMC |
0.3 |
199.585 |
4.43e-45 |
101.848 |
| HMC |
0.5 |
121.952 |
9.24e-35 |
81.065 |
| HMC |
0.9 |
135.355 |
5e-43 |
62.301 |
| HMC |
0.99 |
127.461 |
3.09e-32 |
118.310 |
| SMC |
0.0 |
-0.132 |
0.896 |
-0.045 |
| SMC |
0.3 |
1.253 |
0.218 |
0.451 |
| SMC |
0.5 |
0.772 |
0.445 |
0.247 |
| SMC |
0.9 |
-0.384 |
0.703 |
-0.124 |
| SMC |
0.99 |
1.920 |
0.0635 |
0.773 |
| Metro |
0.0 |
46.124 |
1.82e-21 |
82.323 |
| Metro |
0.3 |
107.831 |
1.17e-30 |
100.642 |
| Metro |
0.5 |
106.253 |
8.29e-32 |
82.333 |
| Metro |
0.9 |
146.222 |
5.22e-46 |
62.951 |
| Metro |
0.99 |
76.650 |
6.61e-26 |
124.033 |
| DEMetro_Z |
0.0 |
11.200 |
8.01e-10 |
71.634 |
| DEMetro_Z |
0.3 |
9.413 |
1.37e-08 |
81.767 |
| DEMetro_Z |
0.5 |
9.670 |
8.83e-09 |
66.296 |
| DEMetro_Z |
0.9 |
113.514 |
1.02e-36 |
62.922 |
| DEMetro_Z |
0.99 |
136.756 |
2.68e-33 |
119.331 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
11.008
|
1.1e-09
|
2.461
|
| DEMetro_Z_vs_SMC |
0.3
|
9.320
|
1.62e-08
|
2.084
|
| DEMetro_Z_vs_SMC |
0.5
|
9.640
|
9.47e-09
|
2.156
|
| DEMetro_Z_vs_SMC |
0.9
|
101.715
|
1.81e-27
|
22.744
|
| DEMetro_Z_vs_SMC |
0.99
|
130.064
|
1.7e-29
|
29.083
|
| HMC_vs_Metro |
0.0
|
1.387
|
0.182
|
0.310
|
| HMC_vs_Metro |
0.3
|
1.432
|
0.169
|
0.320
|
| HMC_vs_Metro |
0.5
|
-1.415
|
0.173
|
-0.316
|
| HMC_vs_Metro |
0.9
|
-1.190
|
0.249
|
-0.266
|
| HMC_vs_Metro |
0.99
|
-2.680
|
0.0148
|
-0.599
|
| Metro_vs_DEMetro_Z |
0.0
|
1.518
|
0.146
|
0.339
|
| Metro_vs_DEMetro_Z |
0.3
|
2.122
|
0.0472
|
0.475
|
| Metro_vs_DEMetro_Z |
0.5
|
2.315
|
0.0319
|
0.518
|
| Metro_vs_DEMetro_Z |
0.9
|
0.047
|
0.963
|
0.010
|
| Metro_vs_DEMetro_Z |
0.99
|
2.281
|
0.0343
|
0.510
|
| HMC_vs_SMC |
0.0
|
153.718
|
7.15e-31
|
34.372
|
| HMC_vs_SMC |
0.3
|
194.272
|
8.38e-33
|
43.441
|
| HMC_vs_SMC |
0.5
|
125.382
|
3.42e-29
|
28.036
|
| HMC_vs_SMC |
0.9
|
136.642
|
6.68e-30
|
30.554
|
| HMC_vs_SMC |
0.99
|
120.917
|
6.8e-29
|
27.038
|
| Metro_vs_SMC |
0.0
|
47.295
|
3.55e-21
|
10.576
|
| Metro_vs_SMC |
0.3
|
110.434
|
3.8e-28
|
24.694
|
| Metro_vs_SMC |
0.5
|
116.485
|
1.38e-28
|
26.047
|
| Metro_vs_SMC |
0.9
|
126.451
|
2.91e-29
|
28.275
|
| Metro_vs_SMC |
0.99
|
82.595
|
9.37e-26
|
18.469
|
| HMC_vs_DEMetro_Z |
0.0
|
2.114
|
0.0479
|
0.473
|
| HMC_vs_DEMetro_Z |
0.3
|
2.306
|
0.0326
|
0.516
|
| HMC_vs_DEMetro_Z |
0.5
|
2.158
|
0.0439
|
0.483
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.967
|
0.345
|
-0.216
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.843
|
0.41
|
-0.189
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.627 |
0.012 |
0.007 |
84.937 |
| HMC |
0.3 |
0.624 |
0.011 |
0.006 |
101.848 |
| HMC |
0.5 |
0.619 |
0.009 |
0.008 |
81.065 |
| HMC |
0.9 |
0.620 |
0.013 |
0.010 |
62.301 |
| HMC |
0.99 |
0.625 |
0.009 |
0.005 |
118.310 |
| SMC |
0.0 |
0.012 |
0.012 |
0.007 |
-0.045 |
| SMC |
0.3 |
0.014 |
0.011 |
0.006 |
0.451 |
| SMC |
0.5 |
0.011 |
0.009 |
0.008 |
0.247 |
| SMC |
0.9 |
0.012 |
0.013 |
0.010 |
-0.124 |
| SMC |
0.99 |
0.013 |
0.009 |
0.005 |
0.773 |
| Metro |
0.0 |
0.608 |
0.012 |
0.007 |
82.323 |
| Metro |
0.3 |
0.616 |
0.011 |
0.006 |
100.642 |
| Metro |
0.5 |
0.628 |
0.009 |
0.008 |
82.333 |
| Metro |
0.9 |
0.626 |
0.013 |
0.010 |
62.951 |
| Metro |
0.99 |
0.655 |
0.009 |
0.005 |
124.033 |
| DEMetro_Z |
0.0 |
0.531 |
0.012 |
0.007 |
71.634 |
| DEMetro_Z |
0.3 |
0.503 |
0.011 |
0.006 |
81.767 |
| DEMetro_Z |
0.5 |
0.508 |
0.009 |
0.008 |
66.296 |
| DEMetro_Z |
0.9 |
0.626 |
0.013 |
0.010 |
62.922 |
| DEMetro_Z |
0.99 |
0.630 |
0.009 |
0.005 |
119.331 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_heavy_Tails_and_high_Dimension
(MvStudentT,
correlation,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.547 |
0.137 |
1.482 |
| HMC |
0.3 |
3.837 |
0.00101 |
4.714 |
| HMC |
0.5 |
3.134 |
0.00534 |
6.150 |
| HMC |
0.9 |
3.045 |
0.00657 |
7.342 |
| HMC |
0.99 |
2.864 |
0.00991 |
15.004 |
| SMC |
0.0 |
37.427 |
1.16e-19 |
70.453 |
| SMC |
0.3 |
62.624 |
1.62e-23 |
427.372 |
| SMC |
0.5 |
37.649 |
2.36e-19 |
222.757 |
| SMC |
0.9 |
118.301 |
1.01e-28 |
2213.543 |
| SMC |
0.99 |
52.424 |
4.32e-22 |
252.879 |
| Metro |
0.0 |
3.803 |
0.00119 |
16.639 |
| Metro |
0.3 |
5.549 |
2.36e-05 |
72.919 |
| Metro |
0.5 |
4.951 |
8.84e-05 |
47.806 |
| Metro |
0.9 |
4.368 |
0.000331 |
926.552 |
| Metro |
0.99 |
5.328 |
3.84e-05 |
1072.032 |
| DEMetro_Z |
0.0 |
19.088 |
7.37e-14 |
314.853 |
| DEMetro_Z |
0.3 |
15.367 |
3.59e-12 |
1018.187 |
| DEMetro_Z |
0.5 |
7.378 |
5.46e-07 |
588.555 |
| DEMetro_Z |
0.9 |
10.397 |
2.8e-09 |
2940.424 |
| DEMetro_Z |
0.99 |
10.260 |
3.47e-09 |
489.219 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-18.961
|
8.38e-14
|
-4.240
|
| HMC_vs_DEMetro_Z |
0.3
|
-15.216
|
4.28e-12
|
-3.402
|
| HMC_vs_DEMetro_Z |
0.5
|
-7.265
|
6.8e-07
|
-1.625
|
| HMC_vs_DEMetro_Z |
0.9
|
-10.372
|
2.91e-09
|
-2.319
|
| HMC_vs_DEMetro_Z |
0.99
|
-9.550
|
1.1e-08
|
-2.135
|
| Metro_vs_SMC |
0.0
|
-10.623
|
1.97e-09
|
-2.375
|
| Metro_vs_SMC |
0.3
|
-23.424
|
1.77e-15
|
-5.238
|
| Metro_vs_SMC |
0.5
|
-15.805
|
2.19e-12
|
-3.534
|
| Metro_vs_SMC |
0.9
|
-5.887
|
1.14e-05
|
-1.316
|
| Metro_vs_SMC |
0.99
|
4.070
|
0.000653
|
0.910
|
| Metro_vs_DEMetro_Z |
0.0
|
-17.844
|
2.51e-13
|
-3.990
|
| Metro_vs_DEMetro_Z |
0.3
|
-13.118
|
5.68e-11
|
-2.933
|
| Metro_vs_DEMetro_Z |
0.5
|
-6.985
|
1.18e-06
|
-1.562
|
| Metro_vs_DEMetro_Z |
0.9
|
-6.305
|
4.73e-06
|
-1.410
|
| Metro_vs_DEMetro_Z |
0.99
|
2.750
|
0.0127
|
0.615
|
| HMC_vs_Metro |
0.0
|
-3.255
|
0.00417
|
-0.728
|
| HMC_vs_Metro |
0.3
|
-5.091
|
6.49e-05
|
-1.138
|
| HMC_vs_Metro |
0.5
|
-4.079
|
0.000639
|
-0.912
|
| HMC_vs_Metro |
0.9
|
-4.324
|
0.000366
|
-0.967
|
| HMC_vs_Metro |
0.99
|
-5.208
|
5e-05
|
-1.165
|
| HMC_vs_SMC |
0.0
|
-31.493
|
7.32e-18
|
-7.042
|
| HMC_vs_SMC |
0.3
|
-59.859
|
4.16e-23
|
-13.385
|
| HMC_vs_SMC |
0.5
|
-32.857
|
3.32e-18
|
-7.347
|
| HMC_vs_SMC |
0.9
|
-118.921
|
9.33e-29
|
-26.592
|
| HMC_vs_SMC |
0.99
|
-33.879
|
1.87e-18
|
-7.576
|
| DEMetro_Z_vs_SMC |
0.0
|
15.502
|
3.08e-12
|
3.466
|
| DEMetro_Z_vs_SMC |
0.3
|
8.838
|
3.7e-08
|
1.976
|
| DEMetro_Z_vs_SMC |
0.5
|
4.715
|
0.000151
|
1.054
|
| DEMetro_Z_vs_SMC |
0.9
|
2.595
|
0.0178
|
0.580
|
| DEMetro_Z_vs_SMC |
0.99
|
4.951
|
8.87e-05
|
1.107
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.101 |
0.068 |
0.022 |
1.482 |
| HMC |
0.3 |
0.177 |
0.067 |
0.023 |
4.714 |
| HMC |
0.5 |
0.196 |
0.067 |
0.021 |
6.150 |
| HMC |
0.9 |
0.286 |
0.049 |
0.032 |
7.342 |
| HMC |
0.99 |
0.723 |
0.053 |
0.045 |
15.004 |
| SMC |
0.0 |
1.617 |
0.068 |
0.022 |
70.453 |
| SMC |
0.3 |
10.003 |
0.067 |
0.023 |
427.372 |
| SMC |
0.5 |
4.746 |
0.067 |
0.021 |
222.757 |
| SMC |
0.9 |
71.715 |
0.049 |
0.032 |
2213.543 |
| SMC |
0.99 |
11.345 |
0.053 |
0.045 |
252.879 |
| Metro |
0.0 |
0.434 |
0.068 |
0.022 |
16.639 |
| Metro |
0.3 |
1.762 |
0.067 |
0.023 |
72.919 |
| Metro |
0.5 |
1.071 |
0.067 |
0.021 |
47.806 |
| Metro |
0.9 |
30.047 |
0.049 |
0.032 |
926.552 |
| Metro |
0.99 |
47.925 |
0.053 |
0.045 |
1072.032 |
| DEMetro_Z |
0.0 |
6.992 |
0.068 |
0.022 |
314.853 |
| DEMetro_Z |
0.3 |
23.738 |
0.067 |
0.023 |
1018.187 |
| DEMetro_Z |
0.5 |
12.428 |
0.067 |
0.021 |
588.555 |
| DEMetro_Z |
0.9 |
95.249 |
0.049 |
0.032 |
2940.424 |
| DEMetro_Z |
0.99 |
21.899 |
0.053 |
0.045 |
489.219 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.030 |
0.976 |
-0.008 |
| HMC |
0.3 |
0.294 |
0.77 |
0.113 |
| HMC |
0.5 |
0.894 |
0.382 |
0.899 |
| HMC |
0.9 |
0.919 |
0.367 |
0.558 |
| HMC |
0.99 |
1.454 |
0.162 |
15.881 |
| SMC |
0.0 |
138.373 |
1.09e-31 |
169.617 |
| SMC |
0.3 |
199.303 |
3.9e-33 |
950.310 |
| SMC |
0.5 |
188.891 |
9.97e-35 |
215.464 |
| SMC |
0.9 |
255.818 |
4.34e-35 |
3552.482 |
| SMC |
0.99 |
265.854 |
2.01e-35 |
2587.428 |
| Metro |
0.0 |
1.608 |
0.124 |
6.164 |
| Metro |
0.3 |
3.492 |
0.00244 |
40.131 |
| Metro |
0.5 |
2.706 |
0.0138 |
4.959 |
| Metro |
0.9 |
3.208 |
0.00463 |
695.544 |
| Metro |
0.99 |
4.686 |
0.000161 |
2886.543 |
| DEMetro_Z |
0.0 |
11.098 |
8.9e-10 |
43.308 |
| DEMetro_Z |
0.3 |
9.928 |
5.91e-09 |
622.821 |
| DEMetro_Z |
0.5 |
15.689 |
2.28e-12 |
67.583 |
| DEMetro_Z |
0.9 |
10.774 |
1.56e-09 |
1309.639 |
| DEMetro_Z |
0.99 |
11.519 |
5.15e-10 |
747.235 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-134.327
|
9.24e-30
|
-30.036
|
| HMC_vs_SMC |
0.3
|
-194.970
|
7.83e-33
|
-43.597
|
| HMC_vs_SMC |
0.5
|
-109.592
|
4.4e-28
|
-24.506
|
| HMC_vs_SMC |
0.9
|
-253.305
|
5.43e-35
|
-56.641
|
| HMC_vs_SMC |
0.99
|
-187.256
|
1.68e-32
|
-41.872
|
| Metro_vs_DEMetro_Z |
0.0
|
-6.901
|
1.4e-06
|
-1.543
|
| Metro_vs_DEMetro_Z |
0.3
|
-8.868
|
3.51e-08
|
-1.983
|
| Metro_vs_DEMetro_Z |
0.5
|
-13.131
|
5.58e-11
|
-2.936
|
| Metro_vs_DEMetro_Z |
0.9
|
-2.172
|
0.0427
|
-0.486
|
| Metro_vs_DEMetro_Z |
0.99
|
3.315
|
0.00364
|
0.741
|
| HMC_vs_Metro |
0.0
|
-1.608
|
0.124
|
-0.359
|
| HMC_vs_Metro |
0.3
|
-3.467
|
0.00258
|
-0.775
|
| HMC_vs_Metro |
0.5
|
-2.457
|
0.0238
|
-0.549
|
| HMC_vs_Metro |
0.9
|
-3.204
|
0.00467
|
-0.717
|
| HMC_vs_Metro |
0.99
|
-4.669
|
0.000167
|
-1.044
|
| HMC_vs_DEMetro_Z |
0.0
|
-11.074
|
9.93e-10
|
-2.476
|
| HMC_vs_DEMetro_Z |
0.3
|
-9.917
|
6.02e-09
|
-2.217
|
| HMC_vs_DEMetro_Z |
0.5
|
-16.068
|
1.63e-12
|
-3.593
|
| HMC_vs_DEMetro_Z |
0.9
|
-10.755
|
1.61e-09
|
-2.405
|
| HMC_vs_DEMetro_Z |
0.99
|
-11.149
|
8.88e-10
|
-2.493
|
| Metro_vs_SMC |
0.0
|
-42.622
|
2.52e-20
|
-9.531
|
| Metro_vs_SMC |
0.3
|
-83.403
|
7.8e-26
|
-18.649
|
| Metro_vs_SMC |
0.5
|
-97.180
|
4.3e-27
|
-21.730
|
| Metro_vs_SMC |
0.9
|
-12.751
|
9.24e-11
|
-2.851
|
| Metro_vs_SMC |
0.99
|
0.484
|
0.634
|
0.108
|
| DEMetro_Z_vs_SMC |
0.0
|
-32.150
|
4.98e-18
|
-7.189
|
| DEMetro_Z_vs_SMC |
0.3
|
-5.183
|
5.29e-05
|
-1.159
|
| DEMetro_Z_vs_SMC |
0.5
|
-30.818
|
1.1e-17
|
-6.891
|
| DEMetro_Z_vs_SMC |
0.9
|
-19.448
|
5.29e-14
|
-4.349
|
| DEMetro_Z_vs_SMC |
0.99
|
-29.575
|
2.36e-17
|
-6.613
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
8.172 |
8.319 |
17.897 |
-0.008 |
| HMC |
0.3 |
10.007 |
8.857 |
10.138 |
0.113 |
| HMC |
0.5 |
16.815 |
8.162 |
9.621 |
0.899 |
| HMC |
0.9 |
11.180 |
6.672 |
8.084 |
0.558 |
| HMC |
0.99 |
28.802 |
2.019 |
1.687 |
15.881 |
| SMC |
0.0 |
3043.966 |
8.319 |
17.897 |
169.617 |
| SMC |
0.3 |
9643.364 |
8.857 |
10.138 |
950.310 |
| SMC |
0.5 |
2081.223 |
8.162 |
9.621 |
215.464 |
| SMC |
0.9 |
28723.815 |
6.672 |
8.084 |
3552.482 |
| SMC |
0.99 |
4365.718 |
2.019 |
1.687 |
2587.428 |
| Metro |
0.0 |
118.630 |
8.319 |
17.897 |
6.164 |
| Metro |
0.3 |
415.711 |
8.857 |
10.138 |
40.131 |
| Metro |
0.5 |
55.872 |
8.162 |
9.621 |
4.959 |
| Metro |
0.9 |
5629.234 |
6.672 |
8.084 |
695.544 |
| Metro |
0.99 |
4870.176 |
2.019 |
1.687 |
2886.543 |
| DEMetro_Z |
0.0 |
783.402 |
8.319 |
17.897 |
43.308 |
| DEMetro_Z |
0.3 |
6323.186 |
8.857 |
10.138 |
622.821 |
| DEMetro_Z |
0.5 |
658.404 |
8.162 |
9.621 |
67.583 |
| DEMetro_Z |
0.9 |
10593.378 |
6.672 |
8.084 |
1309.639 |
| DEMetro_Z |
0.99 |
1262.231 |
2.019 |
1.687 |
747.235 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.904 |
9.11e-05 |
9.146 |
| HMC |
0.3 |
3.269 |
0.00403 |
16.687 |
| HMC |
0.5 |
4.289 |
0.000391 |
16.222 |
| HMC |
0.9 |
4.063 |
0.000656 |
14.861 |
| HMC |
0.99 |
2.881 |
0.00956 |
34.445 |
| SMC |
0.0 |
273.155 |
1.03e-35 |
1510.463 |
| SMC |
0.3 |
379.334 |
2.21e-38 |
2834.413 |
| SMC |
0.5 |
379.231 |
1.89e-38 |
1926.321 |
| SMC |
0.9 |
247.440 |
8.32e-35 |
4865.202 |
| SMC |
0.99 |
374.718 |
2.46e-38 |
2026.869 |
| Metro |
0.0 |
3.603 |
0.0019 |
72.723 |
| Metro |
0.3 |
8.406 |
7.97e-08 |
286.644 |
| Metro |
0.5 |
5.401 |
3.27e-05 |
111.729 |
| Metro |
0.9 |
9.099 |
2.36e-08 |
1397.449 |
| Metro |
0.99 |
7.915 |
1.96e-07 |
2224.237 |
| DEMetro_Z |
0.0 |
23.780 |
1.34e-15 |
693.506 |
| DEMetro_Z |
0.3 |
21.670 |
7.38e-15 |
2178.700 |
| DEMetro_Z |
0.5 |
20.256 |
2.53e-14 |
1120.903 |
| DEMetro_Z |
0.9 |
18.246 |
1.68e-13 |
3610.948 |
| DEMetro_Z |
0.99 |
24.516 |
7.63e-16 |
1185.336 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-18.417
|
1.42e-13
|
-4.118
|
| Metro_vs_DEMetro_Z |
0.3
|
-17.368
|
4.07e-13
|
-3.884
|
| Metro_vs_DEMetro_Z |
0.5
|
-16.048
|
1.67e-12
|
-3.588
|
| Metro_vs_DEMetro_Z |
0.9
|
-8.729
|
4.49e-08
|
-1.952
|
| Metro_vs_DEMetro_Z |
0.99
|
3.379
|
0.00315
|
0.755
|
| DEMetro_Z_vs_SMC |
0.0
|
-28.523
|
4.63e-17
|
-6.378
|
| DEMetro_Z_vs_SMC |
0.3
|
-6.472
|
3.34e-06
|
-1.447
|
| DEMetro_Z_vs_SMC |
0.5
|
-14.398
|
1.13e-11
|
-3.220
|
| DEMetro_Z_vs_SMC |
0.9
|
-6.499
|
3.16e-06
|
-1.453
|
| DEMetro_Z_vs_SMC |
0.99
|
-17.852
|
2.49e-13
|
-3.992
|
| HMC_vs_DEMetro_Z |
0.0
|
-24.130
|
1.02e-15
|
-5.396
|
| HMC_vs_DEMetro_Z |
0.3
|
-21.346
|
9.71e-15
|
-4.773
|
| HMC_vs_DEMetro_Z |
0.5
|
-19.565
|
4.75e-14
|
-4.375
|
| HMC_vs_DEMetro_Z |
0.9
|
-18.083
|
1.97e-13
|
-4.044
|
| HMC_vs_DEMetro_Z |
0.99
|
-22.878
|
2.73e-15
|
-5.116
|
| HMC_vs_Metro |
0.0
|
-3.138
|
0.00541
|
-0.702
|
| HMC_vs_Metro |
0.3
|
-7.696
|
2.97e-07
|
-1.721
|
| HMC_vs_Metro |
0.5
|
-4.685
|
0.000161
|
-1.048
|
| HMC_vs_Metro |
0.9
|
-9.024
|
2.68e-08
|
-2.018
|
| HMC_vs_Metro |
0.99
|
-7.744
|
2.71e-07
|
-1.732
|
| HMC_vs_SMC |
0.0
|
-283.280
|
6.49e-36
|
-63.343
|
| HMC_vs_SMC |
0.3
|
-278.638
|
8.88e-36
|
-62.305
|
| HMC_vs_SMC |
0.5
|
-289.765
|
4.22e-36
|
-64.793
|
| HMC_vs_SMC |
0.9
|
-232.006
|
2.88e-34
|
-51.878
|
| HMC_vs_SMC |
0.99
|
-161.808
|
2.7e-31
|
-36.181
|
| Metro_vs_SMC |
0.0
|
-69.753
|
2.3e-24
|
-15.597
|
| Metro_vs_SMC |
0.3
|
-76.076
|
4.45e-25
|
-17.011
|
| Metro_vs_SMC |
0.5
|
-93.696
|
8.59e-27
|
-20.951
|
| Metro_vs_SMC |
0.9
|
-21.902
|
6.07e-15
|
-4.897
|
| Metro_vs_SMC |
0.99
|
0.700
|
0.492
|
0.157
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.372 |
0.116 |
0.028 |
9.146 |
| HMC |
0.3 |
0.573 |
0.123 |
0.027 |
16.687 |
| HMC |
0.5 |
0.415 |
0.121 |
0.018 |
16.222 |
| HMC |
0.9 |
0.538 |
0.102 |
0.029 |
14.861 |
| HMC |
0.99 |
0.969 |
0.090 |
0.026 |
34.445 |
| SMC |
0.0 |
42.486 |
0.116 |
0.028 |
1510.463 |
| SMC |
0.3 |
76.542 |
0.123 |
0.027 |
2834.413 |
| SMC |
0.5 |
35.088 |
0.121 |
0.018 |
1926.321 |
| SMC |
0.9 |
142.763 |
0.102 |
0.029 |
4865.202 |
| SMC |
0.99 |
51.788 |
0.090 |
0.026 |
2026.869 |
| Metro |
0.0 |
2.156 |
0.116 |
0.028 |
72.723 |
| Metro |
0.3 |
7.851 |
0.123 |
0.027 |
286.644 |
| Metro |
0.5 |
2.149 |
0.121 |
0.018 |
111.729 |
| Metro |
0.9 |
41.079 |
0.102 |
0.029 |
1397.449 |
| Metro |
0.99 |
56.822 |
0.090 |
0.026 |
2224.237 |
| DEMetro_Z |
0.0 |
19.569 |
0.116 |
0.028 |
693.506 |
| DEMetro_Z |
0.3 |
58.863 |
0.123 |
0.027 |
2178.700 |
| DEMetro_Z |
0.5 |
20.468 |
0.121 |
0.018 |
1120.903 |
| DEMetro_Z |
0.9 |
105.985 |
0.102 |
0.029 |
3610.948 |
| DEMetro_Z |
0.99 |
30.324 |
0.090 |
0.026 |
1185.336 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
5.028 |
7.42e-05 |
36.515 |
| HMC |
0.3 |
5.403 |
3.24e-05 |
52.987 |
| HMC |
0.5 |
4.855 |
0.000109 |
28.942 |
| HMC |
0.9 |
7.044 |
1e-06 |
23.777 |
| HMC |
0.99 |
6.304 |
4.54e-06 |
20.887 |
| SMC |
0.0 |
193.589 |
1.17e-34 |
236.612 |
| SMC |
0.3 |
125.998 |
5.75e-30 |
228.615 |
| SMC |
0.5 |
185.066 |
1.83e-35 |
177.699 |
| SMC |
0.9 |
108.614 |
1.12e-29 |
128.330 |
| SMC |
0.99 |
173.956 |
5.33e-44 |
86.818 |
| Metro |
0.0 |
9.293 |
1.68e-08 |
119.168 |
| Metro |
0.3 |
29.685 |
2.11e-17 |
241.201 |
| Metro |
0.5 |
12.651 |
1.04e-10 |
107.251 |
| Metro |
0.9 |
46.399 |
3.97e-21 |
177.141 |
| Metro |
0.99 |
31.623 |
6.08e-18 |
163.485 |
| DEMetro_Z |
0.0 |
57.162 |
8.38e-23 |
277.047 |
| DEMetro_Z |
0.3 |
48.199 |
2.25e-21 |
295.193 |
| DEMetro_Z |
0.5 |
29.040 |
3.19e-17 |
249.591 |
| DEMetro_Z |
0.9 |
26.376 |
1.88e-16 |
188.941 |
| DEMetro_Z |
0.99 |
36.919 |
2.84e-19 |
125.352 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
8.596
|
5.67e-08
|
1.922
|
| DEMetro_Z_vs_SMC |
0.3
|
11.829
|
3.3e-10
|
2.645
|
| DEMetro_Z_vs_SMC |
0.5
|
8.198
|
1.16e-07
|
1.833
|
| DEMetro_Z_vs_SMC |
0.9
|
8.485
|
6.91e-08
|
1.897
|
| DEMetro_Z_vs_SMC |
0.99
|
11.597
|
4.6e-10
|
2.593
|
| HMC_vs_Metro |
0.0
|
-5.546
|
2.38e-05
|
-1.240
|
| HMC_vs_Metro |
0.3
|
-14.173
|
1.49e-11
|
-3.169
|
| HMC_vs_Metro |
0.5
|
-7.122
|
9.01e-07
|
-1.593
|
| HMC_vs_Metro |
0.9
|
-30.753
|
1.14e-17
|
-6.877
|
| HMC_vs_Metro |
0.99
|
-23.726
|
1.4e-15
|
-5.305
|
| Metro_vs_DEMetro_Z |
0.0
|
-10.441
|
2.61e-09
|
-2.335
|
| Metro_vs_DEMetro_Z |
0.3
|
-4.688
|
0.00016
|
-1.048
|
| Metro_vs_DEMetro_Z |
0.5
|
-13.029
|
6.38e-11
|
-2.913
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.420
|
0.172
|
-0.317
|
| Metro_vs_DEMetro_Z |
0.99
|
6.101
|
7.25e-06
|
1.364
|
| HMC_vs_SMC |
0.0
|
-26.655
|
1.63e-16
|
-5.960
|
| HMC_vs_SMC |
0.3
|
-17.788
|
2.65e-13
|
-3.978
|
| HMC_vs_SMC |
0.5
|
-23.649
|
1.48e-15
|
-5.288
|
| HMC_vs_SMC |
0.9
|
-33.378
|
2.47e-18
|
-7.464
|
| HMC_vs_SMC |
0.99
|
-19.715
|
4.13e-14
|
-4.409
|
| Metro_vs_SMC |
0.0
|
-9.041
|
2.6e-08
|
-2.022
|
| Metro_vs_SMC |
0.3
|
1.481
|
0.155
|
0.331
|
| Metro_vs_SMC |
0.5
|
-8.468
|
7.14e-08
|
-1.893
|
| Metro_vs_SMC |
0.9
|
12.648
|
1.06e-10
|
2.828
|
| Metro_vs_SMC |
0.99
|
14.655
|
8.28e-12
|
3.277
|
| HMC_vs_DEMetro_Z |
0.0
|
-27.365
|
1e-16
|
-6.119
|
| HMC_vs_DEMetro_Z |
0.3
|
-19.578
|
4.69e-14
|
-4.378
|
| HMC_vs_DEMetro_Z |
0.5
|
-18.679
|
1.1e-13
|
-4.177
|
| HMC_vs_DEMetro_Z |
0.9
|
-23.253
|
2.02e-15
|
-5.200
|
| HMC_vs_DEMetro_Z |
0.99
|
-19.376
|
5.66e-14
|
-4.333
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.076 |
0.015 |
0.002 |
36.515 |
| HMC |
0.3 |
0.110 |
0.015 |
0.002 |
52.987 |
| HMC |
0.5 |
0.081 |
0.016 |
0.002 |
28.942 |
| HMC |
0.9 |
0.103 |
0.015 |
0.004 |
23.777 |
| HMC |
0.99 |
0.118 |
0.017 |
0.005 |
20.887 |
| SMC |
0.0 |
0.413 |
0.015 |
0.002 |
236.612 |
| SMC |
0.3 |
0.423 |
0.015 |
0.002 |
228.615 |
| SMC |
0.5 |
0.416 |
0.016 |
0.002 |
177.699 |
| SMC |
0.9 |
0.494 |
0.015 |
0.004 |
128.330 |
| SMC |
0.99 |
0.437 |
0.017 |
0.005 |
86.818 |
| Metro |
0.0 |
0.215 |
0.015 |
0.002 |
119.168 |
| Metro |
0.3 |
0.445 |
0.015 |
0.002 |
241.201 |
| Metro |
0.5 |
0.257 |
0.016 |
0.002 |
107.251 |
| Metro |
0.9 |
0.676 |
0.015 |
0.004 |
177.141 |
| Metro |
0.99 |
0.808 |
0.017 |
0.005 |
163.485 |
| DEMetro_Z |
0.0 |
0.481 |
0.015 |
0.002 |
277.047 |
| DEMetro_Z |
0.3 |
0.542 |
0.015 |
0.002 |
295.193 |
| DEMetro_Z |
0.5 |
0.577 |
0.016 |
0.002 |
249.591 |
| DEMetro_Z |
0.9 |
0.720 |
0.015 |
0.004 |
188.941 |
| DEMetro_Z |
0.99 |
0.624 |
0.017 |
0.005 |
125.352 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.005 |
0.0585 |
2.454 |
| HMC |
0.3 |
1.748 |
0.0965 |
7.394 |
| HMC |
0.5 |
3.918 |
0.000606 |
2.318 |
| HMC |
0.9 |
1.812 |
0.0858 |
18.499 |
| HMC |
0.99 |
3.893 |
0.000901 |
5.357 |
| SMC |
0.0 |
24.881 |
3.84e-16 |
60.708 |
| SMC |
0.3 |
40.330 |
6.86e-20 |
381.885 |
| SMC |
0.5 |
24.692 |
6.41e-16 |
184.540 |
| SMC |
0.9 |
52.824 |
4.4e-22 |
1955.218 |
| SMC |
0.99 |
31.105 |
8.8e-18 |
242.006 |
| Metro |
0.0 |
6.701 |
1.43e-06 |
7.772 |
| Metro |
0.3 |
2.892 |
0.00933 |
43.966 |
| Metro |
0.5 |
5.938 |
1.01e-05 |
30.451 |
| Metro |
0.9 |
1.902 |
0.0724 |
1996.428 |
| Metro |
0.99 |
4.537 |
0.000226 |
955.193 |
| DEMetro_Z |
0.0 |
20.857 |
1.47e-14 |
316.493 |
| DEMetro_Z |
0.3 |
9.926 |
5.93e-09 |
1500.214 |
| DEMetro_Z |
0.5 |
6.683 |
2.17e-06 |
725.778 |
| DEMetro_Z |
0.9 |
9.110 |
2.31e-08 |
3661.296 |
| DEMetro_Z |
0.99 |
7.031 |
1.08e-06 |
540.754 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-20.546
|
1.95e-14
|
-4.594
|
| HMC_vs_DEMetro_Z |
0.3
|
-9.836
|
6.87e-09
|
-2.199
|
| HMC_vs_DEMetro_Z |
0.5
|
-6.669
|
2.23e-06
|
-1.491
|
| HMC_vs_DEMetro_Z |
0.9
|
-9.060
|
2.52e-08
|
-2.026
|
| HMC_vs_DEMetro_Z |
0.99
|
-6.981
|
1.19e-06
|
-1.561
|
| Metro_vs_SMC |
0.0
|
-24.332
|
8.78e-16
|
-5.441
|
| Metro_vs_SMC |
0.3
|
-19.400
|
5.54e-14
|
-4.338
|
| Metro_vs_SMC |
0.5
|
-20.308
|
2.41e-14
|
-4.541
|
| Metro_vs_SMC |
0.9
|
0.039
|
0.969
|
0.009
|
| Metro_vs_SMC |
0.99
|
3.387
|
0.0031
|
0.757
|
| Metro_vs_DEMetro_Z |
0.0
|
-20.265
|
2.51e-14
|
-4.531
|
| Metro_vs_DEMetro_Z |
0.3
|
-9.714
|
8.38e-09
|
-2.172
|
| Metro_vs_DEMetro_Z |
0.5
|
-6.320
|
4.58e-06
|
-1.413
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.501
|
0.15
|
-0.336
|
| Metro_vs_DEMetro_Z |
0.99
|
2.162
|
0.0436
|
0.483
|
| HMC_vs_Metro |
0.0
|
-5.244
|
4.62e-05
|
-1.173
|
| HMC_vs_Metro |
0.3
|
-2.221
|
0.0387
|
-0.497
|
| HMC_vs_Metro |
0.5
|
-5.468
|
2.83e-05
|
-1.223
|
| HMC_vs_Metro |
0.9
|
-1.883
|
0.0751
|
-0.421
|
| HMC_vs_Metro |
0.99
|
-4.514
|
0.000237
|
-1.009
|
| HMC_vs_SMC |
0.0
|
-29.432
|
2.58e-17
|
-6.581
|
| HMC_vs_SMC |
0.3
|
-36.477
|
4.69e-19
|
-8.156
|
| HMC_vs_SMC |
0.5
|
-24.102
|
1.05e-15
|
-5.389
|
| HMC_vs_SMC |
0.9
|
-46.305
|
5.29e-21
|
-10.354
|
| HMC_vs_SMC |
0.99
|
-29.504
|
2.47e-17
|
-6.597
|
| DEMetro_Z_vs_SMC |
0.0
|
17.069
|
5.56e-13
|
3.817
|
| DEMetro_Z_vs_SMC |
0.3
|
7.462
|
4.64e-07
|
1.668
|
| DEMetro_Z_vs_SMC |
0.5
|
4.952
|
8.85e-05
|
1.107
|
| DEMetro_Z_vs_SMC |
0.9
|
4.069
|
0.000654
|
0.910
|
| DEMetro_Z_vs_SMC |
0.99
|
3.826
|
0.00114
|
0.856
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.122 |
0.068 |
0.022 |
2.454 |
| HMC |
0.3 |
0.239 |
0.067 |
0.023 |
7.394 |
| HMC |
0.5 |
0.116 |
0.067 |
0.021 |
2.318 |
| HMC |
0.9 |
0.648 |
0.049 |
0.032 |
18.499 |
| HMC |
0.99 |
0.292 |
0.053 |
0.045 |
5.357 |
| SMC |
0.0 |
1.403 |
0.068 |
0.022 |
60.708 |
| SMC |
0.3 |
8.945 |
0.067 |
0.023 |
381.885 |
| SMC |
0.5 |
3.943 |
0.067 |
0.021 |
184.540 |
| SMC |
0.9 |
63.352 |
0.049 |
0.032 |
1955.218 |
| SMC |
0.99 |
10.860 |
0.053 |
0.045 |
242.006 |
| Metro |
0.0 |
0.239 |
0.068 |
0.022 |
7.772 |
| Metro |
0.3 |
1.089 |
0.067 |
0.023 |
43.966 |
| Metro |
0.5 |
0.707 |
0.067 |
0.021 |
30.451 |
| Metro |
0.9 |
64.686 |
0.049 |
0.032 |
1996.428 |
| Metro |
0.99 |
42.708 |
0.053 |
0.045 |
955.193 |
| DEMetro_Z |
0.0 |
7.028 |
0.068 |
0.022 |
316.493 |
| DEMetro_Z |
0.3 |
34.944 |
0.067 |
0.023 |
1500.214 |
| DEMetro_Z |
0.5 |
15.311 |
0.067 |
0.021 |
725.778 |
| DEMetro_Z |
0.9 |
118.588 |
0.049 |
0.032 |
3661.296 |
| DEMetro_Z |
0.99 |
24.201 |
0.053 |
0.045 |
540.754 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.249 |
0.227 |
4.067 |
| HMC |
0.3 |
0.208 |
0.837 |
0.073 |
| HMC |
0.5 |
0.921 |
0.367 |
0.926 |
| HMC |
0.9 |
-0.898 |
0.376 |
-0.237 |
| HMC |
0.99 |
2.289 |
0.0329 |
2.834 |
| SMC |
0.0 |
63.642 |
6.55e-24 |
157.582 |
| SMC |
0.3 |
125.131 |
3.2e-29 |
912.266 |
| SMC |
0.5 |
116.919 |
2.56e-29 |
214.150 |
| SMC |
0.9 |
180.229 |
3.43e-32 |
3634.815 |
| SMC |
0.99 |
196.460 |
6.56e-33 |
2752.926 |
| Metro |
0.0 |
1.776 |
0.0873 |
0.958 |
| Metro |
0.3 |
1.702 |
0.105 |
23.907 |
| Metro |
0.5 |
1.487 |
0.152 |
1.517 |
| Metro |
0.9 |
1.068 |
0.299 |
5242.567 |
| Metro |
0.99 |
2.136 |
0.0459 |
292.004 |
| DEMetro_Z |
0.0 |
7.720 |
2.5e-07 |
17.955 |
| DEMetro_Z |
0.3 |
11.040 |
1.04e-09 |
184.502 |
| DEMetro_Z |
0.5 |
9.223 |
1.65e-08 |
22.831 |
| DEMetro_Z |
0.9 |
9.935 |
5.84e-09 |
370.821 |
| DEMetro_Z |
0.99 |
5.667 |
1.83e-05 |
236.935 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-42.919
|
2.21e-20
|
-9.597
|
| HMC_vs_SMC |
0.3
|
-125.660
|
3.28e-29
|
-28.098
|
| HMC_vs_SMC |
0.5
|
-93.946
|
8.16e-27
|
-21.007
|
| HMC_vs_SMC |
0.9
|
-180.641
|
3.34e-32
|
-40.392
|
| HMC_vs_SMC |
0.99
|
-194.446
|
8.24e-33
|
-43.479
|
| Metro_vs_DEMetro_Z |
0.0
|
-7.476
|
4.52e-07
|
-1.672
|
| Metro_vs_DEMetro_Z |
0.3
|
-7.271
|
6.72e-07
|
-1.626
|
| Metro_vs_DEMetro_Z |
0.5
|
-7.363
|
5.62e-07
|
-1.646
|
| Metro_vs_DEMetro_Z |
0.9
|
0.992
|
0.334
|
0.222
|
| Metro_vs_DEMetro_Z |
0.99
|
0.383
|
0.706
|
0.086
|
| HMC_vs_Metro |
0.0
|
1.093
|
0.288
|
0.244
|
| HMC_vs_Metro |
0.3
|
-1.691
|
0.107
|
-0.378
|
| HMC_vs_Metro |
0.5
|
-1.547
|
0.138
|
-0.346
|
| HMC_vs_Metro |
0.9
|
-1.068
|
0.299
|
-0.239
|
| HMC_vs_Metro |
0.99
|
-2.113
|
0.0481
|
-0.472
|
| HMC_vs_DEMetro_Z |
0.0
|
-4.573
|
0.000208
|
-1.022
|
| HMC_vs_DEMetro_Z |
0.3
|
-10.988
|
1.13e-09
|
-2.457
|
| HMC_vs_DEMetro_Z |
0.5
|
-7.664
|
3.15e-07
|
-1.714
|
| HMC_vs_DEMetro_Z |
0.9
|
-9.932
|
5.87e-09
|
-2.221
|
| HMC_vs_DEMetro_Z |
0.99
|
-5.597
|
2.13e-05
|
-1.251
|
| Metro_vs_SMC |
0.0
|
-64.751
|
9.41e-24
|
-14.479
|
| Metro_vs_SMC |
0.3
|
-65.606
|
7.34e-24
|
-14.670
|
| Metro_vs_SMC |
0.5
|
-93.893
|
8.25e-27
|
-20.995
|
| Metro_vs_SMC |
0.9
|
0.328
|
0.747
|
0.073
|
| Metro_vs_SMC |
0.99
|
-17.673
|
2.98e-13
|
-3.952
|
| DEMetro_Z_vs_SMC |
0.0
|
-45.159
|
8.48e-21
|
-10.098
|
| DEMetro_Z_vs_SMC |
0.3
|
-41.010
|
5.2e-20
|
-9.170
|
| DEMetro_Z_vs_SMC |
0.5
|
-74.533
|
6.56e-25
|
-16.666
|
| DEMetro_Z_vs_SMC |
0.9
|
-80.190
|
1.64e-25
|
-17.931
|
| DEMetro_Z_vs_SMC |
0.99
|
-60.673
|
3.22e-23
|
-13.567
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
81.101 |
8.319 |
17.897 |
4.067 |
| HMC |
0.3 |
9.594 |
8.857 |
10.138 |
0.073 |
| HMC |
0.5 |
17.071 |
8.162 |
9.621 |
0.926 |
| HMC |
0.9 |
4.754 |
6.672 |
8.084 |
-0.237 |
| HMC |
0.99 |
6.798 |
2.019 |
1.687 |
2.834 |
| SMC |
0.0 |
2828.565 |
8.319 |
17.897 |
157.582 |
| SMC |
0.3 |
9257.663 |
8.857 |
10.138 |
912.266 |
| SMC |
0.5 |
2068.582 |
8.162 |
9.621 |
214.150 |
| SMC |
0.9 |
29389.373 |
6.672 |
8.084 |
3634.815 |
| SMC |
0.99 |
4644.831 |
2.019 |
1.687 |
2752.926 |
| Metro |
0.0 |
25.464 |
8.319 |
17.897 |
0.958 |
| Metro |
0.3 |
251.231 |
8.857 |
10.138 |
23.907 |
| Metro |
0.5 |
22.761 |
8.162 |
9.621 |
1.517 |
| Metro |
0.9 |
42385.939 |
6.672 |
8.084 |
5242.567 |
| Metro |
0.99 |
494.484 |
2.019 |
1.687 |
292.004 |
| DEMetro_Z |
0.0 |
329.667 |
8.319 |
17.897 |
17.955 |
| DEMetro_Z |
0.3 |
1879.389 |
8.857 |
10.138 |
184.502 |
| DEMetro_Z |
0.5 |
227.825 |
8.162 |
9.621 |
22.831 |
| DEMetro_Z |
0.9 |
3004.272 |
6.672 |
8.084 |
370.821 |
| DEMetro_Z |
0.99 |
401.610 |
2.019 |
1.687 |
236.935 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.737 |
0.0985 |
40.905 |
| HMC |
0.3 |
2.736 |
0.0131 |
16.205 |
| HMC |
0.5 |
7.555 |
2.29e-07 |
8.346 |
| HMC |
0.9 |
2.301 |
0.0329 |
19.945 |
| HMC |
0.99 |
7.176 |
7.07e-07 |
14.981 |
| SMC |
0.0 |
123.721 |
4.23e-29 |
1453.693 |
| SMC |
0.3 |
219.792 |
7.72e-34 |
2775.463 |
| SMC |
0.5 |
186.686 |
1.68e-32 |
1916.898 |
| SMC |
0.9 |
175.498 |
5.73e-32 |
4791.992 |
| SMC |
0.99 |
250.607 |
6.03e-35 |
2084.988 |
| Metro |
0.0 |
3.850 |
0.00108 |
32.976 |
| Metro |
0.3 |
2.886 |
0.00947 |
124.939 |
| Metro |
0.5 |
5.156 |
5.61e-05 |
56.531 |
| Metro |
0.9 |
2.086 |
0.0507 |
1975.351 |
| Metro |
0.99 |
4.514 |
0.000237 |
1367.419 |
| DEMetro_Z |
0.0 |
15.527 |
2.99e-12 |
436.886 |
| DEMetro_Z |
0.3 |
16.155 |
1.48e-12 |
1517.448 |
| DEMetro_Z |
0.5 |
9.621 |
9.77e-09 |
884.621 |
| DEMetro_Z |
0.9 |
10.593 |
2.06e-09 |
3569.333 |
| DEMetro_Z |
0.99 |
9.899 |
6.2e-09 |
954.946 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-13.269
|
4.66e-11
|
-2.967
|
| Metro_vs_DEMetro_Z |
0.3
|
-13.585
|
3.1e-11
|
-3.038
|
| Metro_vs_DEMetro_Z |
0.5
|
-8.671
|
4.97e-08
|
-1.939
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.604
|
0.125
|
-0.359
|
| Metro_vs_DEMetro_Z |
0.99
|
1.495
|
0.151
|
0.334
|
| DEMetro_Z_vs_SMC |
0.0
|
-35.345
|
8.46e-19
|
-7.903
|
| DEMetro_Z_vs_SMC |
0.3
|
-13.929
|
2.01e-11
|
-3.115
|
| DEMetro_Z_vs_SMC |
0.5
|
-11.552
|
4.92e-10
|
-2.583
|
| DEMetro_Z_vs_SMC |
0.9
|
-3.530
|
0.00224
|
-0.789
|
| DEMetro_Z_vs_SMC |
0.99
|
-11.644
|
4.3e-10
|
-2.604
|
| HMC_vs_DEMetro_Z |
0.0
|
-12.905
|
7.51e-11
|
-2.886
|
| HMC_vs_DEMetro_Z |
0.3
|
-15.763
|
2.29e-12
|
-3.525
|
| HMC_vs_DEMetro_Z |
0.5
|
-9.541
|
1.12e-08
|
-2.133
|
| HMC_vs_DEMetro_Z |
0.9
|
-10.526
|
2.29e-09
|
-2.354
|
| HMC_vs_DEMetro_Z |
0.99
|
-9.735
|
8.09e-09
|
-2.177
|
| HMC_vs_Metro |
0.0
|
0.378
|
0.71
|
0.084
|
| HMC_vs_Metro |
0.3
|
-2.428
|
0.0253
|
-0.543
|
| HMC_vs_Metro |
0.5
|
-4.315
|
0.000374
|
-0.965
|
| HMC_vs_Metro |
0.9
|
-2.063
|
0.053
|
-0.461
|
| HMC_vs_Metro |
0.99
|
-4.465
|
0.000265
|
-0.998
|
| HMC_vs_SMC |
0.0
|
-62.129
|
2.06e-23
|
-13.893
|
| HMC_vs_SMC |
0.3
|
-206.039
|
2.74e-33
|
-46.072
|
| HMC_vs_SMC |
0.5
|
-186.668
|
1.79e-32
|
-41.740
|
| HMC_vs_SMC |
0.9
|
-159.688
|
3.47e-31
|
-35.707
|
| HMC_vs_SMC |
0.99
|
-226.819
|
4.42e-34
|
-50.718
|
| Metro_vs_SMC |
0.0
|
-123.858
|
4.31e-29
|
-27.696
|
| Metro_vs_SMC |
0.3
|
-63.725
|
1.27e-23
|
-14.249
|
| Metro_vs_SMC |
0.5
|
-120.844
|
6.88e-29
|
-27.022
|
| Metro_vs_SMC |
0.9
|
-2.984
|
0.00763
|
-0.667
|
| Metro_vs_SMC |
0.99
|
-2.356
|
0.0294
|
-0.527
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.263 |
0.116 |
0.028 |
40.905 |
| HMC |
0.3 |
0.560 |
0.123 |
0.027 |
16.205 |
| HMC |
0.5 |
0.272 |
0.121 |
0.018 |
8.346 |
| HMC |
0.9 |
0.687 |
0.102 |
0.029 |
19.945 |
| HMC |
0.99 |
0.472 |
0.090 |
0.026 |
14.981 |
| SMC |
0.0 |
40.893 |
0.116 |
0.028 |
1453.693 |
| SMC |
0.3 |
74.952 |
0.123 |
0.027 |
2775.463 |
| SMC |
0.5 |
34.917 |
0.121 |
0.018 |
1916.898 |
| SMC |
0.9 |
140.616 |
0.102 |
0.029 |
4791.992 |
| SMC |
0.99 |
53.270 |
0.090 |
0.026 |
2084.988 |
| Metro |
0.0 |
1.041 |
0.116 |
0.028 |
32.976 |
| Metro |
0.3 |
3.491 |
0.123 |
0.027 |
124.939 |
| Metro |
0.5 |
1.147 |
0.121 |
0.018 |
56.531 |
| Metro |
0.9 |
58.025 |
0.102 |
0.029 |
1975.351 |
| Metro |
0.99 |
34.968 |
0.090 |
0.026 |
1367.419 |
| DEMetro_Z |
0.0 |
12.371 |
0.116 |
0.028 |
436.886 |
| DEMetro_Z |
0.3 |
41.035 |
0.123 |
0.027 |
1517.448 |
| DEMetro_Z |
0.5 |
16.179 |
0.121 |
0.018 |
884.621 |
| DEMetro_Z |
0.9 |
104.764 |
0.102 |
0.029 |
3569.333 |
| DEMetro_Z |
0.99 |
24.447 |
0.090 |
0.026 |
954.946 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.515 |
0.021 |
45.384 |
| HMC |
0.3 |
2.392 |
0.0272 |
63.304 |
| HMC |
0.5 |
5.315 |
3.71e-05 |
12.119 |
| HMC |
0.9 |
2.265 |
0.0354 |
32.722 |
| HMC |
0.99 |
5.599 |
2.07e-05 |
21.031 |
| SMC |
0.0 |
189.825 |
2.14e-34 |
237.597 |
| SMC |
0.3 |
154.038 |
4.9e-32 |
231.790 |
| SMC |
0.5 |
134.967 |
3.27e-31 |
179.563 |
| SMC |
0.9 |
128.937 |
5.97e-32 |
128.293 |
| SMC |
0.99 |
92.047 |
6.35e-29 |
90.726 |
| Metro |
0.0 |
6.772 |
1.8e-06 |
76.173 |
| Metro |
0.3 |
7.786 |
2.49e-07 |
145.202 |
| Metro |
0.5 |
8.018 |
1.61e-07 |
89.341 |
| Metro |
0.9 |
36.624 |
4e-19 |
226.289 |
| Metro |
0.99 |
38.695 |
1.39e-19 |
213.522 |
| DEMetro_Z |
0.0 |
39.799 |
8.69e-20 |
326.030 |
| DEMetro_Z |
0.3 |
32.017 |
5.26e-18 |
371.096 |
| DEMetro_Z |
0.5 |
20.701 |
1.68e-14 |
304.193 |
| DEMetro_Z |
0.9 |
26.561 |
1.68e-16 |
230.226 |
| DEMetro_Z |
0.99 |
19.518 |
4.8e-14 |
153.095 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
10.816
|
1.47e-09
|
2.418
|
| DEMetro_Z_vs_SMC |
0.3
|
12.355
|
1.58e-10
|
2.763
|
| DEMetro_Z_vs_SMC |
0.5
|
8.228
|
1.1e-07
|
1.840
|
| DEMetro_Z_vs_SMC |
0.9
|
11.367
|
6.43e-10
|
2.542
|
| DEMetro_Z_vs_SMC |
0.99
|
7.615
|
3.46e-07
|
1.703
|
| HMC_vs_Metro |
0.0
|
-1.544
|
0.139
|
-0.345
|
| HMC_vs_Metro |
0.3
|
-2.229
|
0.0381
|
-0.498
|
| HMC_vs_Metro |
0.5
|
-6.756
|
1.87e-06
|
-1.511
|
| HMC_vs_Metro |
0.9
|
-11.711
|
3.91e-10
|
-2.619
|
| HMC_vs_Metro |
0.99
|
-29.089
|
3.21e-17
|
-6.504
|
| Metro_vs_DEMetro_Z |
0.0
|
-17.277
|
4.47e-13
|
-3.863
|
| Metro_vs_DEMetro_Z |
0.3
|
-9.829
|
6.95e-09
|
-2.198
|
| Metro_vs_DEMetro_Z |
0.5
|
-9.874
|
6.45e-09
|
-2.208
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.410
|
0.686
|
-0.092
|
| Metro_vs_DEMetro_Z |
0.99
|
8.331
|
9.12e-08
|
1.863
|
| HMC_vs_SMC |
0.0
|
-10.460
|
2.54e-09
|
-2.339
|
| HMC_vs_SMC |
0.3
|
-6.367
|
4.16e-06
|
-1.424
|
| HMC_vs_SMC |
0.5
|
-55.633
|
1.66e-22
|
-12.440
|
| HMC_vs_SMC |
0.9
|
-6.527
|
2.99e-06
|
-1.459
|
| HMC_vs_SMC |
0.99
|
-17.336
|
4.21e-13
|
-3.876
|
| Metro_vs_SMC |
0.0
|
-13.736
|
2.56e-11
|
-3.071
|
| Metro_vs_SMC |
0.3
|
-4.566
|
0.000211
|
-1.021
|
| Metro_vs_SMC |
0.5
|
-7.734
|
2.76e-07
|
-1.729
|
| Metro_vs_SMC |
0.9
|
14.818
|
6.82e-12
|
3.313
|
| Metro_vs_SMC |
0.99
|
21.760
|
6.84e-15
|
4.866
|
| HMC_vs_DEMetro_Z |
0.0
|
-13.353
|
4.18e-11
|
-2.986
|
| HMC_vs_DEMetro_Z |
0.3
|
-9.335
|
1.58e-08
|
-2.087
|
| HMC_vs_DEMetro_Z |
0.5
|
-20.756
|
1.62e-14
|
-4.641
|
| HMC_vs_DEMetro_Z |
0.9
|
-12.146
|
2.11e-10
|
-2.716
|
| HMC_vs_DEMetro_Z |
0.99
|
-14.786
|
7.09e-12
|
-3.306
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.091 |
0.015 |
0.002 |
45.384 |
| HMC |
0.3 |
0.128 |
0.015 |
0.002 |
63.304 |
| HMC |
0.5 |
0.043 |
0.016 |
0.002 |
12.119 |
| HMC |
0.9 |
0.137 |
0.015 |
0.004 |
32.722 |
| HMC |
0.99 |
0.119 |
0.017 |
0.005 |
21.031 |
| SMC |
0.0 |
0.415 |
0.015 |
0.002 |
237.597 |
| SMC |
0.3 |
0.429 |
0.015 |
0.002 |
231.790 |
| SMC |
0.5 |
0.420 |
0.016 |
0.002 |
179.563 |
| SMC |
0.9 |
0.493 |
0.015 |
0.004 |
128.293 |
| SMC |
0.99 |
0.456 |
0.017 |
0.005 |
90.726 |
| Metro |
0.0 |
0.143 |
0.015 |
0.002 |
76.173 |
| Metro |
0.3 |
0.274 |
0.015 |
0.002 |
145.202 |
| Metro |
0.5 |
0.217 |
0.016 |
0.002 |
89.341 |
| Metro |
0.9 |
0.859 |
0.015 |
0.004 |
226.289 |
| Metro |
0.99 |
1.050 |
0.017 |
0.005 |
213.522 |
| DEMetro_Z |
0.0 |
0.563 |
0.015 |
0.002 |
326.030 |
| DEMetro_Z |
0.3 |
0.677 |
0.015 |
0.002 |
371.096 |
| DEMetro_Z |
0.5 |
0.700 |
0.016 |
0.002 |
304.193 |
| DEMetro_Z |
0.9 |
0.874 |
0.015 |
0.004 |
230.226 |
| DEMetro_Z |
0.99 |
0.758 |
0.017 |
0.005 |
153.095 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_only_Dimension
(MvNormal,
dimension,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.560 |
0.579 |
-0.191 |
| HMC |
5 |
-2.410 |
0.0212 |
-0.681 |
| HMC |
10 |
0.478 |
0.635 |
0.154 |
| HMC |
15 |
-1.770 |
0.0849 |
-0.585 |
| HMC |
30 |
-3.698 |
0.000809 |
-1.548 |
| SMC |
2 |
-0.059 |
0.953 |
-0.022 |
| SMC |
5 |
-0.732 |
0.468 |
-0.238 |
| SMC |
10 |
1.185 |
0.244 |
0.438 |
| SMC |
15 |
0.821 |
0.417 |
0.288 |
| SMC |
30 |
1.059 |
0.297 |
0.420 |
| Metro |
2 |
1.373 |
0.181 |
0.675 |
| Metro |
5 |
5.202 |
1.06e-05 |
2.142 |
| Metro |
10 |
7.330 |
2.64e-08 |
3.121 |
| Metro |
15 |
9.052 |
1.99e-09 |
5.260 |
| Metro |
30 |
11.380 |
4.26e-11 |
7.585 |
| DEMetro_Z |
2 |
2.632 |
0.0146 |
1.716 |
| DEMetro_Z |
5 |
8.382 |
8.32e-08 |
400.100 |
| DEMetro_Z |
10 |
16.764 |
7.67e-13 |
1086.421 |
| DEMetro_Z |
15 |
25.432 |
3.88e-16 |
2086.429 |
| DEMetro_Z |
30 |
25.736 |
3.11e-16 |
3275.468 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.494
|
0.022
|
-0.558
|
| HMC_vs_DEMetro_Z |
1
|
-8.410
|
7.91e-08
|
-1.881
|
| HMC_vs_DEMetro_Z |
2
|
-16.744
|
7.83e-13
|
-3.744
|
| HMC_vs_DEMetro_Z |
3
|
-25.436
|
3.87e-16
|
-5.688
|
| HMC_vs_DEMetro_Z |
4
|
-25.726
|
3.14e-16
|
-5.752
|
| Metro_vs_SMC |
0
|
1.334
|
0.198
|
0.298
|
| Metro_vs_SMC |
1
|
4.844
|
0.000113
|
1.083
|
| Metro_vs_SMC |
2
|
9.108
|
2.32e-08
|
2.037
|
| Metro_vs_SMC |
3
|
8.293
|
9.78e-08
|
1.854
|
| Metro_vs_SMC |
4
|
10.267
|
3.43e-09
|
2.296
|
| Metro_vs_DEMetro_Z |
0
|
-1.355
|
0.191
|
-0.303
|
| Metro_vs_DEMetro_Z |
1
|
-8.347
|
8.87e-08
|
-1.866
|
| Metro_vs_DEMetro_Z |
2
|
-16.706
|
8.16e-13
|
-3.735
|
| Metro_vs_DEMetro_Z |
3
|
-25.327
|
4.19e-16
|
-5.663
|
| Metro_vs_DEMetro_Z |
4
|
-25.693
|
3.21e-16
|
-5.745
|
| HMC_vs_Metro |
0
|
-1.803
|
0.0873
|
-0.403
|
| HMC_vs_Metro |
1
|
-7.295
|
6.41e-07
|
-1.631
|
| HMC_vs_Metro |
2
|
-6.771
|
1.82e-06
|
-1.514
|
| HMC_vs_Metro |
3
|
-11.024
|
1.07e-09
|
-2.465
|
| HMC_vs_Metro |
4
|
-14.525
|
9.68e-12
|
-3.248
|
| HMC_vs_SMC |
0
|
-0.705
|
0.489
|
-0.158
|
| HMC_vs_SMC |
1
|
-2.177
|
0.0423
|
-0.487
|
| HMC_vs_SMC |
2
|
-0.924
|
0.367
|
-0.207
|
| HMC_vs_SMC |
3
|
-3.171
|
0.00503
|
-0.709
|
| HMC_vs_SMC |
4
|
-5.265
|
4.41e-05
|
-1.177
|
| DEMetro_Z_vs_SMC |
0
|
2.303
|
0.0328
|
0.515
|
| DEMetro_Z_vs_SMC |
1
|
8.400
|
8.07e-08
|
1.878
|
| DEMetro_Z_vs_SMC |
2
|
16.762
|
7.68e-13
|
3.748
|
| DEMetro_Z_vs_SMC |
3
|
25.448
|
3.84e-16
|
5.690
|
| DEMetro_Z_vs_SMC |
4
|
25.716
|
3.16e-16
|
5.750
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.020 |
0.022 |
0.010 |
-0.191 |
| HMC |
5 |
0.017 |
0.021 |
0.007 |
-0.681 |
| HMC |
10 |
0.021 |
0.020 |
0.004 |
0.154 |
| HMC |
15 |
0.020 |
0.022 |
0.003 |
-0.585 |
| HMC |
30 |
0.019 |
0.022 |
0.002 |
-1.548 |
| SMC |
2 |
0.022 |
0.022 |
0.010 |
-0.022 |
| SMC |
5 |
0.020 |
0.021 |
0.007 |
-0.238 |
| SMC |
10 |
0.022 |
0.020 |
0.004 |
0.438 |
| SMC |
15 |
0.023 |
0.022 |
0.003 |
0.288 |
| SMC |
30 |
0.023 |
0.022 |
0.002 |
0.420 |
| Metro |
2 |
0.029 |
0.022 |
0.010 |
0.675 |
| Metro |
5 |
0.036 |
0.021 |
0.007 |
2.142 |
| Metro |
10 |
0.034 |
0.020 |
0.004 |
3.121 |
| Metro |
15 |
0.037 |
0.022 |
0.003 |
5.260 |
| Metro |
30 |
0.037 |
0.022 |
0.002 |
7.585 |
| DEMetro_Z |
2 |
0.039 |
0.022 |
0.010 |
1.716 |
| DEMetro_Z |
5 |
2.737 |
0.021 |
0.007 |
400.100 |
| DEMetro_Z |
10 |
4.728 |
0.020 |
0.004 |
1086.421 |
| DEMetro_Z |
15 |
6.044 |
0.022 |
0.003 |
2086.429 |
| DEMetro_Z |
30 |
6.662 |
0.022 |
0.002 |
3275.468 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.927 |
0.36 |
0.333 |
| HMC |
5 |
1.926 |
0.0618 |
0.656 |
| HMC |
10 |
2.726 |
0.0103 |
1.149 |
| HMC |
15 |
5.439 |
3.82e-06 |
1.943 |
| HMC |
30 |
7.744 |
5.98e-09 |
3.096 |
| SMC |
2 |
-1.403 |
0.169 |
-0.400 |
| SMC |
5 |
0.334 |
0.741 |
0.124 |
| SMC |
10 |
-0.254 |
0.801 |
-0.083 |
| SMC |
15 |
1.670 |
0.103 |
0.538 |
| SMC |
30 |
3.382 |
0.0019 |
1.401 |
| Metro |
2 |
2.103 |
0.044 |
0.959 |
| Metro |
5 |
4.204 |
0.000239 |
2.072 |
| Metro |
10 |
7.393 |
5e-08 |
3.729 |
| Metro |
15 |
9.572 |
1.28e-10 |
4.366 |
| Metro |
30 |
14.583 |
2.77e-16 |
5.614 |
| DEMetro_Z |
2 |
4.893 |
2.59e-05 |
2.005 |
| DEMetro_Z |
5 |
8.509 |
6.63e-08 |
4485.842 |
| DEMetro_Z |
10 |
17.048 |
5.68e-13 |
22618.876 |
| DEMetro_Z |
15 |
14.972 |
5.69e-12 |
22728.928 |
| DEMetro_Z |
30 |
23.532 |
1.63e-15 |
42747.862 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
2.451
|
0.0241
|
0.548
|
| HMC_vs_SMC |
1
|
1.280
|
0.216
|
0.286
|
| HMC_vs_SMC |
2
|
2.629
|
0.0165
|
0.588
|
| HMC_vs_SMC |
3
|
4.624
|
0.000185
|
1.034
|
| HMC_vs_SMC |
4
|
3.450
|
0.00268
|
0.771
|
| Metro_vs_DEMetro_Z |
0
|
-2.766
|
0.0123
|
-0.618
|
| Metro_vs_DEMetro_Z |
1
|
-8.501
|
6.72e-08
|
-1.901
|
| Metro_vs_DEMetro_Z |
2
|
-17.045
|
5.7e-13
|
-3.811
|
| Metro_vs_DEMetro_Z |
3
|
-14.969
|
5.71e-12
|
-3.347
|
| Metro_vs_DEMetro_Z |
4
|
-23.528
|
1.63e-15
|
-5.261
|
| HMC_vs_Metro |
0
|
-1.286
|
0.214
|
-0.287
|
| HMC_vs_Metro |
1
|
-2.990
|
0.00753
|
-0.669
|
| HMC_vs_Metro |
2
|
-4.335
|
0.000357
|
-0.969
|
| HMC_vs_Metro |
3
|
-5.210
|
4.99e-05
|
-1.165
|
| HMC_vs_Metro |
4
|
-5.723
|
1.62e-05
|
-1.280
|
| HMC_vs_DEMetro_Z |
0
|
-3.281
|
0.00393
|
-0.734
|
| HMC_vs_DEMetro_Z |
1
|
-8.507
|
6.65e-08
|
-1.902
|
| HMC_vs_DEMetro_Z |
2
|
-17.047
|
5.69e-13
|
-3.812
|
| HMC_vs_DEMetro_Z |
3
|
-14.970
|
5.7e-12
|
-3.347
|
| HMC_vs_DEMetro_Z |
4
|
-23.530
|
1.63e-15
|
-5.261
|
| Metro_vs_SMC |
0
|
3.668
|
0.00164
|
0.820
|
| Metro_vs_SMC |
1
|
3.599
|
0.00191
|
0.805
|
| Metro_vs_SMC |
2
|
7.273
|
6.7e-07
|
1.626
|
| Metro_vs_SMC |
3
|
8.316
|
9.38e-08
|
1.860
|
| Metro_vs_SMC |
4
|
11.157
|
8.78e-10
|
2.495
|
| DEMetro_Z_vs_SMC |
0
|
7.000
|
1.15e-06
|
1.565
|
| DEMetro_Z_vs_SMC |
1
|
8.508
|
6.64e-08
|
1.902
|
| DEMetro_Z_vs_SMC |
2
|
17.048
|
5.68e-13
|
3.812
|
| DEMetro_Z_vs_SMC |
3
|
14.972
|
5.69e-12
|
3.348
|
| DEMetro_Z_vs_SMC |
4
|
23.531
|
1.63e-15
|
5.262
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.036 |
0.031 |
0.016 |
0.333 |
| HMC |
5 |
0.036 |
0.031 |
0.009 |
0.656 |
| HMC |
10 |
0.037 |
0.031 |
0.006 |
1.149 |
| HMC |
15 |
0.042 |
0.030 |
0.006 |
1.943 |
| HMC |
30 |
0.043 |
0.031 |
0.004 |
3.096 |
| SMC |
2 |
0.024 |
0.031 |
0.016 |
-0.400 |
| SMC |
5 |
0.032 |
0.031 |
0.009 |
0.124 |
| SMC |
10 |
0.030 |
0.031 |
0.006 |
-0.083 |
| SMC |
15 |
0.033 |
0.030 |
0.006 |
0.538 |
| SMC |
30 |
0.037 |
0.031 |
0.004 |
1.401 |
| Metro |
2 |
0.046 |
0.031 |
0.016 |
0.959 |
| Metro |
5 |
0.049 |
0.031 |
0.009 |
2.072 |
| Metro |
10 |
0.052 |
0.031 |
0.006 |
3.729 |
| Metro |
15 |
0.058 |
0.030 |
0.006 |
4.366 |
| Metro |
30 |
0.052 |
0.031 |
0.004 |
5.614 |
| DEMetro_Z |
2 |
0.063 |
0.031 |
0.016 |
2.005 |
| DEMetro_Z |
5 |
38.385 |
0.031 |
0.009 |
4485.842 |
| DEMetro_Z |
10 |
128.127 |
0.031 |
0.006 |
22618.876 |
| DEMetro_Z |
15 |
146.588 |
0.030 |
0.006 |
22728.928 |
| DEMetro_Z |
30 |
156.922 |
0.031 |
0.004 |
42747.862 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.500 |
0.621 |
-0.197 |
| HMC |
5 |
-0.918 |
0.365 |
-0.260 |
| HMC |
10 |
1.716 |
0.0943 |
0.541 |
| HMC |
15 |
0.905 |
0.371 |
0.310 |
| HMC |
30 |
0.727 |
0.472 |
0.252 |
| SMC |
2 |
-0.043 |
0.966 |
-0.019 |
| SMC |
5 |
0.577 |
0.567 |
0.172 |
| SMC |
10 |
1.058 |
0.297 |
0.333 |
| SMC |
15 |
1.175 |
0.248 |
0.411 |
| SMC |
30 |
2.294 |
0.0278 |
0.846 |
| Metro |
2 |
3.844 |
0.000779 |
2.487 |
| Metro |
5 |
6.920 |
9.08e-08 |
3.009 |
| Metro |
10 |
8.771 |
7.07e-10 |
3.862 |
| Metro |
15 |
11.821 |
1.51e-11 |
7.541 |
| Metro |
30 |
12.696 |
2.76e-12 |
7.870 |
| DEMetro_Z |
2 |
6.363 |
1.94e-06 |
4.944 |
| DEMetro_Z |
5 |
14.427 |
1.09e-11 |
879.007 |
| DEMetro_Z |
10 |
27.663 |
8.18e-17 |
2920.873 |
| DEMetro_Z |
15 |
27.443 |
9.48e-17 |
5740.503 |
| DEMetro_Z |
30 |
35.888 |
6.36e-19 |
7039.566 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.495
|
0.022
|
-0.558
|
| Metro_vs_DEMetro_Z |
1
|
-14.370
|
1.17e-11
|
-3.213
|
| Metro_vs_DEMetro_Z |
2
|
-27.584
|
8.62e-17
|
-6.168
|
| Metro_vs_DEMetro_Z |
3
|
-27.408
|
9.71e-17
|
-6.129
|
| Metro_vs_DEMetro_Z |
4
|
-35.861
|
6.45e-19
|
-8.019
|
| DEMetro_Z_vs_SMC |
0
|
5.767
|
1.48e-05
|
1.290
|
| DEMetro_Z_vs_SMC |
1
|
14.427
|
1.09e-11
|
3.226
|
| DEMetro_Z_vs_SMC |
2
|
27.641
|
8.3e-17
|
6.181
|
| DEMetro_Z_vs_SMC |
3
|
27.453
|
9.42e-17
|
6.139
|
| DEMetro_Z_vs_SMC |
4
|
35.858
|
6.46e-19
|
8.018
|
| HMC_vs_DEMetro_Z |
0
|
-6.383
|
4.02e-06
|
-1.427
|
| HMC_vs_DEMetro_Z |
1
|
-14.448
|
1.06e-11
|
-3.231
|
| HMC_vs_DEMetro_Z |
2
|
-27.626
|
8.38e-17
|
-6.177
|
| HMC_vs_DEMetro_Z |
3
|
-27.456
|
9.4e-17
|
-6.139
|
| HMC_vs_DEMetro_Z |
4
|
-35.861
|
6.45e-19
|
-8.019
|
| HMC_vs_Metro |
0
|
-4.456
|
0.000271
|
-0.996
|
| HMC_vs_Metro |
1
|
-8.884
|
3.41e-08
|
-1.987
|
| HMC_vs_Metro |
2
|
-8.376
|
8.42e-08
|
-1.873
|
| HMC_vs_Metro |
3
|
-11.703
|
3.95e-10
|
-2.617
|
| HMC_vs_Metro |
4
|
-13.077
|
5.99e-11
|
-2.924
|
| HMC_vs_SMC |
0
|
-0.496
|
0.625
|
-0.111
|
| HMC_vs_SMC |
1
|
-2.333
|
0.0308
|
-0.522
|
| HMC_vs_SMC |
2
|
1.101
|
0.284
|
0.246
|
| HMC_vs_SMC |
3
|
-0.314
|
0.757
|
-0.070
|
| HMC_vs_SMC |
4
|
-2.025
|
0.0571
|
-0.453
|
| Metro_vs_SMC |
0
|
3.613
|
0.00185
|
0.808
|
| Metro_vs_SMC |
1
|
6.724
|
2e-06
|
1.503
|
| Metro_vs_SMC |
2
|
11.078
|
9.87e-10
|
2.477
|
| Metro_vs_SMC |
3
|
10.479
|
2.46e-09
|
2.343
|
| Metro_vs_SMC |
4
|
11.487
|
5.4e-10
|
2.569
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.030 |
0.030 |
0.005 |
-0.197 |
| HMC |
5 |
0.027 |
0.028 |
0.004 |
-0.260 |
| HMC |
10 |
0.029 |
0.028 |
0.003 |
0.541 |
| HMC |
15 |
0.029 |
0.029 |
0.002 |
0.310 |
| HMC |
30 |
0.029 |
0.028 |
0.001 |
0.252 |
| SMC |
2 |
0.030 |
0.030 |
0.005 |
-0.019 |
| SMC |
5 |
0.029 |
0.028 |
0.004 |
0.172 |
| SMC |
10 |
0.029 |
0.028 |
0.003 |
0.333 |
| SMC |
15 |
0.029 |
0.029 |
0.002 |
0.411 |
| SMC |
30 |
0.030 |
0.028 |
0.001 |
0.846 |
| Metro |
2 |
0.042 |
0.030 |
0.005 |
2.487 |
| Metro |
5 |
0.041 |
0.028 |
0.004 |
3.009 |
| Metro |
10 |
0.039 |
0.028 |
0.003 |
3.862 |
| Metro |
15 |
0.041 |
0.029 |
0.002 |
7.541 |
| Metro |
30 |
0.040 |
0.028 |
0.001 |
7.870 |
| DEMetro_Z |
2 |
0.054 |
0.030 |
0.005 |
4.944 |
| DEMetro_Z |
5 |
3.881 |
0.028 |
0.004 |
879.007 |
| DEMetro_Z |
10 |
8.587 |
0.028 |
0.003 |
2920.873 |
| DEMetro_Z |
15 |
9.336 |
0.029 |
0.002 |
5740.503 |
| DEMetro_Z |
30 |
9.935 |
0.028 |
0.001 |
7039.566 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.454 |
0.652 |
-0.169 |
| HMC |
5 |
-1.058 |
0.297 |
-0.295 |
| HMC |
10 |
1.219 |
0.23 |
0.425 |
| HMC |
15 |
0.200 |
0.843 |
0.068 |
| HMC |
30 |
-1.262 |
0.215 |
-0.458 |
| SMC |
2 |
-0.439 |
0.663 |
-0.159 |
| SMC |
5 |
0.260 |
0.796 |
0.079 |
| SMC |
10 |
0.936 |
0.356 |
0.361 |
| SMC |
15 |
1.182 |
0.245 |
0.389 |
| SMC |
30 |
1.196 |
0.24 |
0.481 |
| Metro |
2 |
4.095 |
0.000331 |
2.077 |
| Metro |
5 |
6.710 |
9.79e-08 |
2.574 |
| Metro |
10 |
8.559 |
1.08e-09 |
3.700 |
| Metro |
15 |
10.170 |
1.97e-10 |
5.938 |
| Metro |
30 |
11.336 |
5.74e-11 |
7.883 |
| DEMetro_Z |
2 |
5.041 |
4.09e-05 |
3.538 |
| DEMetro_Z |
5 |
37.477 |
2.41e-19 |
168.500 |
| DEMetro_Z |
10 |
39.381 |
1.05e-19 |
289.487 |
| DEMetro_Z |
15 |
53.383 |
3.38e-22 |
402.136 |
| DEMetro_Z |
30 |
64.766 |
8.84e-24 |
554.466 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.827
|
0.000117
|
1.079
|
| DEMetro_Z_vs_SMC |
1
|
37.495
|
2.8e-19
|
8.384
|
| DEMetro_Z_vs_SMC |
2
|
39.903
|
8.69e-20
|
8.923
|
| DEMetro_Z_vs_SMC |
3
|
53.091
|
4.01e-22
|
11.872
|
| DEMetro_Z_vs_SMC |
4
|
65.354
|
7.9e-24
|
14.614
|
| HMC_vs_Metro |
0
|
-4.908
|
9.77e-05
|
-1.097
|
| HMC_vs_Metro |
1
|
-8.088
|
1.42e-07
|
-1.809
|
| HMC_vs_Metro |
2
|
-7.049
|
1.04e-06
|
-1.576
|
| HMC_vs_Metro |
3
|
-11.170
|
8.61e-10
|
-2.498
|
| HMC_vs_Metro |
4
|
-12.453
|
1.38e-10
|
-2.785
|
| Metro_vs_DEMetro_Z |
0
|
-1.738
|
0.0984
|
-0.389
|
| Metro_vs_DEMetro_Z |
1
|
-37.359
|
2.99e-19
|
-8.354
|
| Metro_vs_DEMetro_Z |
2
|
-39.516
|
1.04e-19
|
-8.836
|
| Metro_vs_DEMetro_Z |
3
|
-52.991
|
4.16e-22
|
-11.849
|
| Metro_vs_DEMetro_Z |
4
|
-63.044
|
1.56e-23
|
-14.097
|
| HMC_vs_SMC |
0
|
-0.034
|
0.973
|
-0.008
|
| HMC_vs_SMC |
1
|
-1.934
|
0.0681
|
-0.433
|
| HMC_vs_SMC |
2
|
0.204
|
0.84
|
0.046
|
| HMC_vs_SMC |
3
|
-1.015
|
0.323
|
-0.227
|
| HMC_vs_SMC |
4
|
-2.888
|
0.00942
|
-0.646
|
| Metro_vs_SMC |
0
|
4.365
|
0.000333
|
0.976
|
| Metro_vs_SMC |
1
|
6.268
|
5.11e-06
|
1.402
|
| Metro_vs_SMC |
2
|
11.731
|
3.8e-10
|
2.623
|
| Metro_vs_SMC |
3
|
9.070
|
2.48e-08
|
2.028
|
| Metro_vs_SMC |
4
|
11.214
|
8.07e-10
|
2.507
|
| HMC_vs_DEMetro_Z |
0
|
-5.516
|
2.55e-05
|
-1.233
|
| HMC_vs_DEMetro_Z |
1
|
-38.365
|
1.82e-19
|
-8.579
|
| HMC_vs_DEMetro_Z |
2
|
-39.941
|
8.54e-20
|
-8.931
|
| HMC_vs_DEMetro_Z |
3
|
-52.953
|
4.21e-22
|
-11.841
|
| HMC_vs_DEMetro_Z |
4
|
-65.263
|
8.11e-24
|
-14.593
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.014 |
0.015 |
0.004 |
-0.169 |
| HMC |
5 |
0.013 |
0.014 |
0.003 |
-0.295 |
| HMC |
10 |
0.014 |
0.013 |
0.002 |
0.425 |
| HMC |
15 |
0.014 |
0.014 |
0.001 |
0.068 |
| HMC |
30 |
0.014 |
0.014 |
0.001 |
-0.458 |
| SMC |
2 |
0.014 |
0.015 |
0.004 |
-0.159 |
| SMC |
5 |
0.014 |
0.014 |
0.003 |
0.079 |
| SMC |
10 |
0.014 |
0.013 |
0.002 |
0.361 |
| SMC |
15 |
0.014 |
0.014 |
0.001 |
0.389 |
| SMC |
30 |
0.015 |
0.014 |
0.001 |
0.481 |
| Metro |
2 |
0.022 |
0.015 |
0.004 |
2.077 |
| Metro |
5 |
0.022 |
0.014 |
0.003 |
2.574 |
| Metro |
10 |
0.021 |
0.013 |
0.002 |
3.700 |
| Metro |
15 |
0.022 |
0.014 |
0.001 |
5.938 |
| Metro |
30 |
0.022 |
0.014 |
0.001 |
7.883 |
| DEMetro_Z |
2 |
0.028 |
0.015 |
0.004 |
3.538 |
| DEMetro_Z |
5 |
0.580 |
0.014 |
0.003 |
168.500 |
| DEMetro_Z |
10 |
0.602 |
0.013 |
0.002 |
289.487 |
| DEMetro_Z |
15 |
0.579 |
0.014 |
0.001 |
402.136 |
| DEMetro_Z |
30 |
0.587 |
0.014 |
0.001 |
554.466 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.695 |
0.0982 |
-0.535 |
| HMC |
5 |
-1.481 |
0.147 |
-0.451 |
| HMC |
10 |
-0.027 |
0.979 |
-0.009 |
| HMC |
15 |
-2.304 |
0.027 |
-0.807 |
| HMC |
30 |
-3.180 |
0.0031 |
-1.213 |
| SMC |
2 |
-0.597 |
0.555 |
-0.235 |
| SMC |
5 |
-0.816 |
0.42 |
-0.228 |
| SMC |
10 |
-0.605 |
0.549 |
-0.212 |
| SMC |
15 |
-0.115 |
0.909 |
-0.053 |
| SMC |
30 |
0.507 |
0.616 |
0.208 |
| Metro |
2 |
1.496 |
0.146 |
0.734 |
| Metro |
5 |
5.095 |
1.79e-05 |
2.324 |
| Metro |
10 |
9.651 |
2.39e-11 |
3.681 |
| Metro |
15 |
9.850 |
2.74e-10 |
5.451 |
| Metro |
30 |
12.746 |
1.49e-12 |
7.382 |
| DEMetro_Z |
2 |
3.395 |
0.00209 |
1.713 |
| DEMetro_Z |
5 |
5.015 |
7.68e-05 |
204.052 |
| DEMetro_Z |
10 |
9.427 |
1.35e-08 |
1511.209 |
| DEMetro_Z |
15 |
13.948 |
1.96e-11 |
2894.908 |
| DEMetro_Z |
30 |
18.117 |
1.91e-13 |
5531.884 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-4.913
|
9.65e-05
|
-1.099
|
| HMC_vs_DEMetro_Z |
1
|
-5.028
|
7.47e-05
|
-1.124
|
| HMC_vs_DEMetro_Z |
2
|
-9.428
|
1.35e-08
|
-2.108
|
| HMC_vs_DEMetro_Z |
3
|
-13.951
|
1.96e-11
|
-3.119
|
| HMC_vs_DEMetro_Z |
4
|
-18.121
|
1.9e-13
|
-4.052
|
| Metro_vs_SMC |
0
|
1.851
|
0.0798
|
0.414
|
| Metro_vs_SMC |
1
|
6.296
|
4.82e-06
|
1.408
|
| Metro_vs_SMC |
2
|
9.756
|
7.83e-09
|
2.181
|
| Metro_vs_SMC |
3
|
11.618
|
4.46e-10
|
2.598
|
| Metro_vs_SMC |
4
|
9.471
|
1.25e-08
|
2.118
|
| Metro_vs_DEMetro_Z |
0
|
-1.582
|
0.13
|
-0.354
|
| Metro_vs_DEMetro_Z |
1
|
-4.951
|
8.86e-05
|
-1.107
|
| Metro_vs_DEMetro_Z |
2
|
-9.404
|
1.4e-08
|
-2.103
|
| Metro_vs_DEMetro_Z |
3
|
-13.921
|
2.03e-11
|
-3.113
|
| Metro_vs_DEMetro_Z |
4
|
-18.097
|
1.94e-13
|
-4.047
|
| HMC_vs_Metro |
0
|
-3.006
|
0.00726
|
-0.672
|
| HMC_vs_Metro |
1
|
-6.121
|
6.96e-06
|
-1.369
|
| HMC_vs_Metro |
2
|
-11.098
|
9.58e-10
|
-2.482
|
| HMC_vs_Metro |
3
|
-12.361
|
1.57e-10
|
-2.764
|
| HMC_vs_Metro |
4
|
-14.265
|
1.33e-11
|
-3.190
|
| HMC_vs_SMC |
0
|
-1.109
|
0.281
|
-0.248
|
| HMC_vs_SMC |
1
|
-0.808
|
0.429
|
-0.181
|
| HMC_vs_SMC |
2
|
0.765
|
0.454
|
0.171
|
| HMC_vs_SMC |
3
|
-1.875
|
0.0762
|
-0.419
|
| HMC_vs_SMC |
4
|
-3.574
|
0.00203
|
-0.799
|
| DEMetro_Z_vs_SMC |
0
|
4.131
|
0.000568
|
0.924
|
| DEMetro_Z_vs_SMC |
1
|
5.021
|
7.58e-05
|
1.123
|
| DEMetro_Z_vs_SMC |
2
|
9.430
|
1.34e-08
|
2.109
|
| DEMetro_Z_vs_SMC |
3
|
13.957
|
1.94e-11
|
3.121
|
| DEMetro_Z_vs_SMC |
4
|
18.111
|
1.92e-13
|
4.050
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.017 |
0.022 |
0.010 |
-0.535 |
| HMC |
5 |
0.018 |
0.021 |
0.007 |
-0.451 |
| HMC |
10 |
0.020 |
0.020 |
0.004 |
-0.009 |
| HMC |
15 |
0.020 |
0.022 |
0.003 |
-0.807 |
| HMC |
30 |
0.019 |
0.022 |
0.002 |
-1.213 |
| SMC |
2 |
0.020 |
0.022 |
0.010 |
-0.235 |
| SMC |
5 |
0.020 |
0.021 |
0.007 |
-0.228 |
| SMC |
10 |
0.019 |
0.020 |
0.004 |
-0.212 |
| SMC |
15 |
0.022 |
0.022 |
0.003 |
-0.053 |
| SMC |
30 |
0.022 |
0.022 |
0.002 |
0.208 |
| Metro |
2 |
0.029 |
0.022 |
0.010 |
0.734 |
| Metro |
5 |
0.037 |
0.021 |
0.007 |
2.324 |
| Metro |
10 |
0.036 |
0.020 |
0.004 |
3.681 |
| Metro |
15 |
0.038 |
0.022 |
0.003 |
5.451 |
| Metro |
30 |
0.037 |
0.022 |
0.002 |
7.382 |
| DEMetro_Z |
2 |
0.039 |
0.022 |
0.010 |
1.713 |
| DEMetro_Z |
5 |
1.406 |
0.021 |
0.007 |
204.052 |
| DEMetro_Z |
10 |
6.568 |
0.020 |
0.004 |
1511.209 |
| DEMetro_Z |
15 |
8.377 |
0.022 |
0.003 |
2894.908 |
| DEMetro_Z |
30 |
11.237 |
0.022 |
0.002 |
5531.884 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.040 |
0.968 |
0.014 |
| HMC |
5 |
2.587 |
0.0138 |
0.903 |
| HMC |
10 |
1.352 |
0.185 |
0.461 |
| HMC |
15 |
4.965 |
1.54e-05 |
1.683 |
| HMC |
30 |
10.853 |
5.78e-13 |
3.859 |
| SMC |
2 |
-0.227 |
0.821 |
-0.069 |
| SMC |
5 |
-1.302 |
0.201 |
-0.380 |
| SMC |
10 |
-0.657 |
0.515 |
-0.214 |
| SMC |
15 |
2.051 |
0.0477 |
0.577 |
| SMC |
30 |
-0.557 |
0.581 |
-0.210 |
| Metro |
2 |
1.882 |
0.069 |
0.798 |
| Metro |
5 |
4.053 |
0.000407 |
2.261 |
| Metro |
10 |
6.639 |
4.4e-07 |
3.598 |
| Metro |
15 |
8.752 |
3.41e-10 |
3.452 |
| Metro |
30 |
12.163 |
1.06e-12 |
6.050 |
| DEMetro_Z |
2 |
3.167 |
0.00329 |
1.263 |
| DEMetro_Z |
5 |
3.358 |
0.00331 |
1626.274 |
| DEMetro_Z |
10 |
6.680 |
2.19e-06 |
4194.707 |
| DEMetro_Z |
15 |
11.746 |
3.72e-10 |
3256.878 |
| DEMetro_Z |
30 |
13.257 |
4.73e-11 |
6365.104 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.309
|
0.761
|
0.069
|
| HMC_vs_SMC |
1
|
4.165
|
0.000526
|
0.931
|
| HMC_vs_SMC |
2
|
1.931
|
0.0685
|
0.432
|
| HMC_vs_SMC |
3
|
4.066
|
0.000659
|
0.909
|
| HMC_vs_SMC |
4
|
9.433
|
1.34e-08
|
2.109
|
| Metro_vs_DEMetro_Z |
0
|
-0.780
|
0.445
|
-0.174
|
| Metro_vs_DEMetro_Z |
1
|
-3.354
|
0.00333
|
-0.750
|
| Metro_vs_DEMetro_Z |
2
|
-6.675
|
2.21e-06
|
-1.493
|
| Metro_vs_DEMetro_Z |
3
|
-11.732
|
3.79e-10
|
-2.623
|
| Metro_vs_DEMetro_Z |
4
|
-13.249
|
4.78e-11
|
-2.962
|
| HMC_vs_Metro |
0
|
-1.925
|
0.0694
|
-0.430
|
| HMC_vs_Metro |
1
|
-2.358
|
0.0293
|
-0.527
|
| HMC_vs_Metro |
2
|
-6.085
|
7.49e-06
|
-1.361
|
| HMC_vs_Metro |
3
|
-4.432
|
0.000286
|
-0.991
|
| HMC_vs_Metro |
4
|
-4.496
|
0.000247
|
-1.005
|
| HMC_vs_DEMetro_Z |
0
|
-2.984
|
0.00763
|
-0.667
|
| HMC_vs_DEMetro_Z |
1
|
-3.357
|
0.00331
|
-0.751
|
| HMC_vs_DEMetro_Z |
2
|
-6.679
|
2.19e-06
|
-1.493
|
| HMC_vs_DEMetro_Z |
3
|
-11.738
|
3.76e-10
|
-2.625
|
| HMC_vs_DEMetro_Z |
4
|
-13.251
|
4.77e-11
|
-2.963
|
| Metro_vs_SMC |
0
|
2.209
|
0.0396
|
0.494
|
| Metro_vs_SMC |
1
|
5.761
|
1.5e-05
|
1.288
|
| Metro_vs_SMC |
2
|
9.031
|
2.65e-08
|
2.019
|
| Metro_vs_SMC |
3
|
7.558
|
3.86e-07
|
1.690
|
| Metro_vs_SMC |
4
|
11.070
|
9.99e-10
|
2.475
|
| DEMetro_Z_vs_SMC |
0
|
3.821
|
0.00115
|
0.854
|
| DEMetro_Z_vs_SMC |
1
|
3.359
|
0.0033
|
0.751
|
| DEMetro_Z_vs_SMC |
2
|
6.681
|
2.18e-06
|
1.494
|
| DEMetro_Z_vs_SMC |
3
|
11.744
|
3.73e-10
|
2.626
|
| DEMetro_Z_vs_SMC |
4
|
13.257
|
4.73e-11
|
2.964
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.031 |
0.031 |
0.016 |
0.014 |
| HMC |
5 |
0.039 |
0.031 |
0.009 |
0.903 |
| HMC |
10 |
0.033 |
0.031 |
0.006 |
0.461 |
| HMC |
15 |
0.041 |
0.030 |
0.006 |
1.683 |
| HMC |
30 |
0.046 |
0.031 |
0.004 |
3.859 |
| SMC |
2 |
0.030 |
0.031 |
0.016 |
-0.069 |
| SMC |
5 |
0.028 |
0.031 |
0.009 |
-0.380 |
| SMC |
10 |
0.029 |
0.031 |
0.006 |
-0.214 |
| SMC |
15 |
0.033 |
0.030 |
0.006 |
0.577 |
| SMC |
30 |
0.031 |
0.031 |
0.004 |
-0.210 |
| Metro |
2 |
0.043 |
0.031 |
0.016 |
0.798 |
| Metro |
5 |
0.050 |
0.031 |
0.009 |
2.261 |
| Metro |
10 |
0.051 |
0.031 |
0.006 |
3.598 |
| Metro |
15 |
0.052 |
0.030 |
0.006 |
3.452 |
| Metro |
30 |
0.054 |
0.031 |
0.004 |
6.050 |
| DEMetro_Z |
2 |
0.051 |
0.031 |
0.016 |
1.263 |
| DEMetro_Z |
5 |
13.936 |
0.031 |
0.009 |
1626.274 |
| DEMetro_Z |
10 |
23.786 |
0.031 |
0.006 |
4194.707 |
| DEMetro_Z |
15 |
21.030 |
0.030 |
0.006 |
3256.878 |
| DEMetro_Z |
30 |
23.392 |
0.031 |
0.004 |
6365.104 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.883 |
0.0675 |
-0.640 |
| HMC |
5 |
0.538 |
0.594 |
0.159 |
| HMC |
10 |
1.704 |
0.0967 |
0.507 |
| HMC |
15 |
0.446 |
0.658 |
0.164 |
| HMC |
30 |
1.665 |
0.104 |
0.559 |
| SMC |
2 |
-0.309 |
0.759 |
-0.162 |
| SMC |
5 |
-0.424 |
0.674 |
-0.122 |
| SMC |
10 |
-0.397 |
0.694 |
-0.125 |
| SMC |
15 |
-0.140 |
0.89 |
-0.068 |
| SMC |
30 |
0.785 |
0.438 |
0.279 |
| Metro |
2 |
3.318 |
0.00294 |
2.269 |
| Metro |
5 |
6.498 |
6.63e-07 |
3.578 |
| Metro |
10 |
10.114 |
1.13e-11 |
4.058 |
| Metro |
15 |
10.937 |
1.2e-10 |
7.655 |
| Metro |
30 |
13.335 |
5.76e-13 |
7.773 |
| DEMetro_Z |
2 |
5.581 |
1.17e-05 |
4.167 |
| DEMetro_Z |
5 |
4.779 |
0.00013 |
283.342 |
| DEMetro_Z |
10 |
9.537 |
1.12e-08 |
1960.023 |
| DEMetro_Z |
15 |
14.148 |
1.53e-11 |
4453.952 |
| DEMetro_Z |
30 |
18.434 |
1.39e-13 |
6718.672 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.020
|
0.0577
|
-0.452
|
| Metro_vs_DEMetro_Z |
1
|
-4.715
|
0.000151
|
-1.054
|
| Metro_vs_DEMetro_Z |
2
|
-9.517
|
1.16e-08
|
-2.128
|
| Metro_vs_DEMetro_Z |
3
|
-14.124
|
1.58e-11
|
-3.158
|
| Metro_vs_DEMetro_Z |
4
|
-18.415
|
1.42e-13
|
-4.118
|
| DEMetro_Z_vs_SMC |
0
|
5.730
|
1.6e-05
|
1.281
|
| DEMetro_Z_vs_SMC |
1
|
4.780
|
0.00013
|
1.069
|
| DEMetro_Z_vs_SMC |
2
|
9.540
|
1.12e-08
|
2.133
|
| DEMetro_Z_vs_SMC |
3
|
14.157
|
1.52e-11
|
3.166
|
| DEMetro_Z_vs_SMC |
4
|
18.428
|
1.4e-13
|
4.121
|
| HMC_vs_DEMetro_Z |
0
|
-6.896
|
1.41e-06
|
-1.542
|
| HMC_vs_DEMetro_Z |
1
|
-4.777
|
0.000131
|
-1.068
|
| HMC_vs_DEMetro_Z |
2
|
-9.536
|
1.13e-08
|
-2.132
|
| HMC_vs_DEMetro_Z |
3
|
-14.145
|
1.54e-11
|
-3.163
|
| HMC_vs_DEMetro_Z |
4
|
-18.430
|
1.4e-13
|
-4.121
|
| HMC_vs_Metro |
0
|
-4.208
|
0.000476
|
-0.941
|
| HMC_vs_Metro |
1
|
-6.236
|
5.46e-06
|
-1.394
|
| HMC_vs_Metro |
2
|
-11.519
|
5.16e-10
|
-2.576
|
| HMC_vs_Metro |
3
|
-10.516
|
2.33e-09
|
-2.351
|
| HMC_vs_Metro |
4
|
-11.428
|
5.89e-10
|
-2.555
|
| HMC_vs_SMC |
0
|
-1.232
|
0.233
|
-0.276
|
| HMC_vs_SMC |
1
|
0.985
|
0.337
|
0.220
|
| HMC_vs_SMC |
2
|
2.856
|
0.0101
|
0.639
|
| HMC_vs_SMC |
3
|
0.462
|
0.649
|
0.103
|
| HMC_vs_SMC |
4
|
0.921
|
0.368
|
0.206
|
| Metro_vs_SMC |
0
|
3.123
|
0.0056
|
0.698
|
| Metro_vs_SMC |
1
|
7.291
|
6.47e-07
|
1.630
|
| Metro_vs_SMC |
2
|
12.290
|
1.73e-10
|
2.748
|
| Metro_vs_SMC |
3
|
12.665
|
1.04e-10
|
2.832
|
| Metro_vs_SMC |
4
|
10.644
|
1.91e-09
|
2.380
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.027 |
0.030 |
0.005 |
-0.640 |
| HMC |
5 |
0.029 |
0.028 |
0.004 |
0.159 |
| HMC |
10 |
0.029 |
0.028 |
0.003 |
0.507 |
| HMC |
15 |
0.029 |
0.029 |
0.002 |
0.164 |
| HMC |
30 |
0.029 |
0.028 |
0.001 |
0.559 |
| SMC |
2 |
0.030 |
0.030 |
0.005 |
-0.162 |
| SMC |
5 |
0.028 |
0.028 |
0.004 |
-0.122 |
| SMC |
10 |
0.027 |
0.028 |
0.003 |
-0.125 |
| SMC |
15 |
0.028 |
0.029 |
0.002 |
-0.068 |
| SMC |
30 |
0.029 |
0.028 |
0.001 |
0.279 |
| Metro |
2 |
0.041 |
0.030 |
0.005 |
2.269 |
| Metro |
5 |
0.044 |
0.028 |
0.004 |
3.578 |
| Metro |
10 |
0.040 |
0.028 |
0.003 |
4.058 |
| Metro |
15 |
0.041 |
0.029 |
0.002 |
7.655 |
| Metro |
30 |
0.039 |
0.028 |
0.001 |
7.773 |
| DEMetro_Z |
2 |
0.051 |
0.030 |
0.005 |
4.167 |
| DEMetro_Z |
5 |
1.270 |
0.028 |
0.004 |
283.342 |
| DEMetro_Z |
10 |
5.772 |
0.028 |
0.003 |
1960.023 |
| DEMetro_Z |
15 |
7.250 |
0.029 |
0.002 |
4453.952 |
| DEMetro_Z |
30 |
9.483 |
0.028 |
0.001 |
6718.672 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.158 |
0.254 |
-0.373 |
| HMC |
5 |
-0.095 |
0.925 |
-0.027 |
| HMC |
10 |
1.073 |
0.29 |
0.355 |
| HMC |
15 |
-0.320 |
0.751 |
-0.114 |
| HMC |
30 |
-0.298 |
0.768 |
-0.113 |
| SMC |
2 |
-0.378 |
0.708 |
-0.175 |
| SMC |
5 |
-0.845 |
0.403 |
-0.239 |
| SMC |
10 |
-0.274 |
0.786 |
-0.099 |
| SMC |
15 |
-0.125 |
0.901 |
-0.059 |
| SMC |
30 |
0.365 |
0.717 |
0.140 |
| Metro |
2 |
3.069 |
0.00494 |
1.681 |
| Metro |
5 |
5.599 |
5.19e-06 |
2.742 |
| Metro |
10 |
10.402 |
5.82e-12 |
4.197 |
| Metro |
15 |
11.227 |
1.55e-11 |
6.145 |
| Metro |
30 |
12.786 |
2.43e-12 |
7.954 |
| DEMetro_Z |
2 |
4.444 |
0.000171 |
2.902 |
| DEMetro_Z |
5 |
8.922 |
3.14e-08 |
62.706 |
| DEMetro_Z |
10 |
19.456 |
5.23e-14 |
390.316 |
| DEMetro_Z |
15 |
97.343 |
3.68e-27 |
618.023 |
| DEMetro_Z |
30 |
39.727 |
9.39e-20 |
914.123 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.443
|
0.000279
|
0.994
|
| DEMetro_Z_vs_SMC |
1
|
8.938
|
3.11e-08
|
1.999
|
| DEMetro_Z_vs_SMC |
2
|
19.505
|
5.02e-14
|
4.361
|
| DEMetro_Z_vs_SMC |
3
|
97.764
|
3.84e-27
|
21.861
|
| DEMetro_Z_vs_SMC |
4
|
39.616
|
9.96e-20
|
8.858
|
| HMC_vs_Metro |
0
|
-3.787
|
0.00125
|
-0.847
|
| HMC_vs_Metro |
1
|
-5.939
|
1.02e-05
|
-1.328
|
| HMC_vs_Metro |
2
|
-11.479
|
5.46e-10
|
-2.567
|
| HMC_vs_Metro |
3
|
-12.210
|
1.93e-10
|
-2.730
|
| HMC_vs_Metro |
4
|
-13.105
|
5.77e-11
|
-2.930
|
| Metro_vs_DEMetro_Z |
0
|
-1.582
|
0.13
|
-0.354
|
| Metro_vs_DEMetro_Z |
1
|
-8.354
|
8.76e-08
|
-1.868
|
| Metro_vs_DEMetro_Z |
2
|
-19.162
|
6.92e-14
|
-4.285
|
| Metro_vs_DEMetro_Z |
3
|
-92.955
|
9.98e-27
|
-20.785
|
| Metro_vs_DEMetro_Z |
4
|
-39.777
|
9.23e-20
|
-8.894
|
| HMC_vs_SMC |
0
|
-0.579
|
0.569
|
-0.129
|
| HMC_vs_SMC |
1
|
0.783
|
0.443
|
0.175
|
| HMC_vs_SMC |
2
|
1.643
|
0.117
|
0.367
|
| HMC_vs_SMC |
3
|
-0.126
|
0.901
|
-0.028
|
| HMC_vs_SMC |
4
|
-0.714
|
0.484
|
-0.160
|
| Metro_vs_SMC |
0
|
2.846
|
0.0103
|
0.636
|
| Metro_vs_SMC |
1
|
6.672
|
2.22e-06
|
1.492
|
| Metro_vs_SMC |
2
|
11.013
|
1.09e-09
|
2.463
|
| Metro_vs_SMC |
3
|
13.261
|
4.71e-11
|
2.965
|
| Metro_vs_SMC |
4
|
10.448
|
2.58e-09
|
2.336
|
| HMC_vs_DEMetro_Z |
0
|
-5.245
|
4.61e-05
|
-1.173
|
| HMC_vs_DEMetro_Z |
1
|
-8.960
|
2.99e-08
|
-2.004
|
| HMC_vs_DEMetro_Z |
2
|
-19.379
|
5.65e-14
|
-4.333
|
| HMC_vs_DEMetro_Z |
3
|
-97.336
|
4.17e-27
|
-21.765
|
| HMC_vs_DEMetro_Z |
4
|
-39.664
|
9.74e-20
|
-8.869
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.013 |
0.015 |
0.004 |
-0.373 |
| HMC |
5 |
0.014 |
0.014 |
0.003 |
-0.027 |
| HMC |
10 |
0.014 |
0.013 |
0.002 |
0.355 |
| HMC |
15 |
0.014 |
0.014 |
0.001 |
-0.114 |
| HMC |
30 |
0.014 |
0.014 |
0.001 |
-0.113 |
| SMC |
2 |
0.014 |
0.015 |
0.004 |
-0.175 |
| SMC |
5 |
0.013 |
0.014 |
0.003 |
-0.239 |
| SMC |
10 |
0.013 |
0.013 |
0.002 |
-0.099 |
| SMC |
15 |
0.014 |
0.014 |
0.001 |
-0.059 |
| SMC |
30 |
0.014 |
0.014 |
0.001 |
0.140 |
| Metro |
2 |
0.021 |
0.015 |
0.004 |
1.681 |
| Metro |
5 |
0.023 |
0.014 |
0.003 |
2.742 |
| Metro |
10 |
0.022 |
0.013 |
0.002 |
4.197 |
| Metro |
15 |
0.023 |
0.014 |
0.001 |
6.145 |
| Metro |
30 |
0.022 |
0.014 |
0.001 |
7.954 |
| DEMetro_Z |
2 |
0.025 |
0.015 |
0.004 |
2.902 |
| DEMetro_Z |
5 |
0.225 |
0.014 |
0.003 |
62.706 |
| DEMetro_Z |
10 |
0.807 |
0.013 |
0.002 |
390.316 |
| DEMetro_Z |
15 |
0.882 |
0.014 |
0.001 |
618.023 |
| DEMetro_Z |
30 |
0.959 |
0.014 |
0.001 |
914.123 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_correlation
(MvNormal,
dimension,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.327 |
0.195 |
0.636 |
| HMC |
5 |
1.959 |
0.0609 |
1.087 |
| HMC |
10 |
4.428 |
0.0002 |
3.341 |
| HMC |
15 |
2.416 |
0.0239 |
1.668 |
| HMC |
30 |
4.535 |
0.000195 |
5.534 |
| SMC |
2 |
-0.636 |
0.528 |
-0.224 |
| SMC |
5 |
-0.087 |
0.931 |
-0.029 |
| SMC |
10 |
2.065 |
0.0459 |
0.696 |
| SMC |
15 |
-0.325 |
0.747 |
-0.111 |
| SMC |
30 |
-1.992 |
0.0546 |
-0.538 |
| Metro |
2 |
4.734 |
0.000103 |
4.014 |
| Metro |
5 |
6.903 |
1.32e-06 |
21.813 |
| Metro |
10 |
4.479 |
0.000254 |
18.473 |
| Metro |
15 |
5.128 |
5.89e-05 |
23.742 |
| Metro |
30 |
4.909 |
9.64e-05 |
24.075 |
| DEMetro_Z |
2 |
2.966 |
0.00628 |
1.588 |
| DEMetro_Z |
5 |
9.044 |
2.59e-08 |
710.197 |
| DEMetro_Z |
10 |
16.089 |
1.59e-12 |
584.626 |
| DEMetro_Z |
15 |
26.746 |
1.52e-16 |
558.223 |
| DEMetro_Z |
30 |
31.546 |
7.02e-18 |
527.068 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.685
|
0.108
|
-0.377
|
| HMC_vs_DEMetro_Z |
1
|
-9.026
|
2.67e-08
|
-2.018
|
| HMC_vs_DEMetro_Z |
2
|
-16.021
|
1.72e-12
|
-3.582
|
| HMC_vs_DEMetro_Z |
3
|
-26.888
|
1.38e-16
|
-6.012
|
| HMC_vs_DEMetro_Z |
4
|
-30.762
|
1.13e-17
|
-6.879
|
| Metro_vs_SMC |
0
|
5.049
|
7.13e-05
|
1.129
|
| Metro_vs_SMC |
1
|
6.962
|
1.24e-06
|
1.557
|
| Metro_vs_SMC |
2
|
4.361
|
0.000336
|
0.975
|
| Metro_vs_SMC |
3
|
5.233
|
4.74e-05
|
1.170
|
| Metro_vs_SMC |
4
|
5.080
|
6.66e-05
|
1.136
|
| Metro_vs_DEMetro_Z |
0
|
2.316
|
0.0319
|
0.518
|
| Metro_vs_DEMetro_Z |
1
|
-8.847
|
3.65e-08
|
-1.978
|
| Metro_vs_DEMetro_Z |
2
|
-15.692
|
2.48e-12
|
-3.509
|
| Metro_vs_DEMetro_Z |
3
|
-25.278
|
4.34e-16
|
-5.652
|
| Metro_vs_DEMetro_Z |
4
|
-28.179
|
5.8e-17
|
-6.301
|
| HMC_vs_Metro |
0
|
-4.013
|
0.000744
|
-0.897
|
| HMC_vs_Metro |
1
|
-6.436
|
3.6e-06
|
-1.439
|
| HMC_vs_Metro |
2
|
-3.577
|
0.00201
|
-0.800
|
| HMC_vs_Metro |
3
|
-4.634
|
0.000181
|
-1.036
|
| HMC_vs_Metro |
4
|
-3.552
|
0.00213
|
-0.794
|
| HMC_vs_SMC |
0
|
1.567
|
0.134
|
0.350
|
| HMC_vs_SMC |
1
|
2.296
|
0.0332
|
0.513
|
| HMC_vs_SMC |
2
|
3.630
|
0.00178
|
0.812
|
| HMC_vs_SMC |
3
|
2.373
|
0.0284
|
0.531
|
| HMC_vs_SMC |
4
|
5.096
|
6.41e-05
|
1.140
|
| DEMetro_Z_vs_SMC |
0
|
3.261
|
0.00411
|
0.729
|
| DEMetro_Z_vs_SMC |
1
|
9.047
|
2.57e-08
|
2.023
|
| DEMetro_Z_vs_SMC |
2
|
16.044
|
1.68e-12
|
3.588
|
| DEMetro_Z_vs_SMC |
3
|
26.753
|
1.52e-16
|
5.982
|
| DEMetro_Z_vs_SMC |
4
|
31.556
|
7.05e-18
|
7.056
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.030 |
0.022 |
0.013 |
0.636 |
| HMC |
5 |
0.031 |
0.019 |
0.011 |
1.087 |
| HMC |
10 |
0.050 |
0.016 |
0.010 |
3.341 |
| HMC |
15 |
0.039 |
0.020 |
0.011 |
1.668 |
| HMC |
30 |
0.094 |
0.022 |
0.013 |
5.534 |
| SMC |
2 |
0.019 |
0.022 |
0.013 |
-0.224 |
| SMC |
5 |
0.019 |
0.019 |
0.011 |
-0.029 |
| SMC |
10 |
0.023 |
0.016 |
0.010 |
0.696 |
| SMC |
15 |
0.019 |
0.020 |
0.011 |
-0.111 |
| SMC |
30 |
0.015 |
0.022 |
0.013 |
-0.538 |
| Metro |
2 |
0.074 |
0.022 |
0.013 |
4.014 |
| Metro |
5 |
0.254 |
0.019 |
0.011 |
21.813 |
| Metro |
10 |
0.200 |
0.016 |
0.010 |
18.473 |
| Metro |
15 |
0.279 |
0.020 |
0.011 |
23.742 |
| Metro |
30 |
0.336 |
0.022 |
0.013 |
24.075 |
| DEMetro_Z |
2 |
0.043 |
0.022 |
0.013 |
1.588 |
| DEMetro_Z |
5 |
7.668 |
0.019 |
0.011 |
710.197 |
| DEMetro_Z |
10 |
5.834 |
0.016 |
0.010 |
584.626 |
| DEMetro_Z |
15 |
6.101 |
0.020 |
0.011 |
558.223 |
| DEMetro_Z |
30 |
6.888 |
0.022 |
0.013 |
527.068 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.901 |
0.00731 |
1.517 |
| HMC |
5 |
4.218 |
0.000371 |
3.835 |
| HMC |
10 |
2.975 |
0.00694 |
2.378 |
| HMC |
15 |
4.143 |
0.000396 |
3.013 |
| HMC |
30 |
3.645 |
0.0016 |
4.842 |
| SMC |
2 |
1.829 |
0.0761 |
0.696 |
| SMC |
5 |
1.601 |
0.12 |
0.707 |
| SMC |
10 |
0.808 |
0.425 |
0.368 |
| SMC |
15 |
-0.155 |
0.877 |
-0.050 |
| SMC |
30 |
1.728 |
0.0934 |
0.714 |
| Metro |
2 |
5.976 |
5.12e-06 |
4.901 |
| Metro |
5 |
4.504 |
0.000234 |
10.804 |
| Metro |
10 |
4.420 |
0.000291 |
20.475 |
| Metro |
15 |
6.811 |
1.25e-06 |
9.267 |
| Metro |
30 |
5.913 |
1.04e-05 |
20.353 |
| DEMetro_Z |
2 |
3.079 |
0.00534 |
2.278 |
| DEMetro_Z |
5 |
6.250 |
5.31e-06 |
11979.745 |
| DEMetro_Z |
10 |
16.936 |
6.39e-13 |
17277.565 |
| DEMetro_Z |
15 |
19.392 |
5.58e-14 |
10967.145 |
| DEMetro_Z |
30 |
31.112 |
9.19e-18 |
13017.017 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.318
|
0.203
|
0.295
|
| HMC_vs_SMC |
1
|
3.181
|
0.00492
|
0.711
|
| HMC_vs_SMC |
2
|
2.217
|
0.039
|
0.496
|
| HMC_vs_SMC |
3
|
3.933
|
0.000893
|
0.879
|
| HMC_vs_SMC |
4
|
3.276
|
0.00397
|
0.733
|
| Metro_vs_DEMetro_Z |
0
|
2.616
|
0.017
|
0.585
|
| Metro_vs_DEMetro_Z |
1
|
-6.243
|
5.38e-06
|
-1.396
|
| Metro_vs_DEMetro_Z |
2
|
-16.926
|
6.46e-13
|
-3.785
|
| Metro_vs_DEMetro_Z |
3
|
-19.374
|
5.67e-14
|
-4.332
|
| Metro_vs_DEMetro_Z |
4
|
-31.037
|
9.6e-18
|
-6.940
|
| HMC_vs_Metro |
0
|
-4.598
|
0.000196
|
-1.028
|
| HMC_vs_Metro |
1
|
-2.883
|
0.00952
|
-0.645
|
| HMC_vs_Metro |
2
|
-3.835
|
0.00112
|
-0.858
|
| HMC_vs_Metro |
3
|
-3.649
|
0.00171
|
-0.816
|
| HMC_vs_Metro |
4
|
-4.516
|
0.000237
|
-1.010
|
| HMC_vs_DEMetro_Z |
0
|
-0.861
|
0.4
|
-0.193
|
| HMC_vs_DEMetro_Z |
1
|
-6.247
|
5.34e-06
|
-1.397
|
| HMC_vs_DEMetro_Z |
2
|
-16.932
|
6.42e-13
|
-3.786
|
| HMC_vs_DEMetro_Z |
3
|
-19.395
|
5.56e-14
|
-4.337
|
| HMC_vs_DEMetro_Z |
4
|
-31.126
|
9.1e-18
|
-6.960
|
| Metro_vs_SMC |
0
|
4.981
|
8.3e-05
|
1.114
|
| Metro_vs_SMC |
1
|
4.372
|
0.000328
|
0.978
|
| Metro_vs_SMC |
2
|
4.373
|
0.000327
|
0.978
|
| Metro_vs_SMC |
3
|
7.584
|
3.67e-07
|
1.696
|
| Metro_vs_SMC |
4
|
5.537
|
2.43e-05
|
1.238
|
| DEMetro_Z_vs_SMC |
0
|
2.018
|
0.058
|
0.451
|
| DEMetro_Z_vs_SMC |
1
|
6.250
|
5.31e-06
|
1.397
|
| DEMetro_Z_vs_SMC |
2
|
16.934
|
6.41e-13
|
3.786
|
| DEMetro_Z_vs_SMC |
3
|
19.390
|
5.59e-14
|
4.336
|
| DEMetro_Z_vs_SMC |
4
|
31.116
|
9.16e-18
|
6.958
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.035 |
0.019 |
0.010 |
1.517 |
| HMC |
5 |
0.056 |
0.022 |
0.009 |
3.835 |
| HMC |
10 |
0.045 |
0.024 |
0.009 |
2.378 |
| HMC |
15 |
0.069 |
0.024 |
0.015 |
3.013 |
| HMC |
30 |
0.089 |
0.025 |
0.013 |
4.842 |
| SMC |
2 |
0.027 |
0.019 |
0.010 |
0.696 |
| SMC |
5 |
0.028 |
0.022 |
0.009 |
0.707 |
| SMC |
10 |
0.028 |
0.024 |
0.009 |
0.368 |
| SMC |
15 |
0.023 |
0.024 |
0.015 |
-0.050 |
| SMC |
30 |
0.035 |
0.025 |
0.013 |
0.714 |
| Metro |
2 |
0.070 |
0.019 |
0.010 |
4.901 |
| Metro |
5 |
0.119 |
0.022 |
0.009 |
10.804 |
| Metro |
10 |
0.206 |
0.024 |
0.009 |
20.475 |
| Metro |
15 |
0.161 |
0.024 |
0.015 |
9.267 |
| Metro |
30 |
0.292 |
0.025 |
0.013 |
20.353 |
| DEMetro_Z |
2 |
0.043 |
0.019 |
0.010 |
2.278 |
| DEMetro_Z |
5 |
107.500 |
0.022 |
0.009 |
11979.745 |
| DEMetro_Z |
10 |
153.178 |
0.024 |
0.009 |
17277.565 |
| DEMetro_Z |
15 |
161.695 |
0.024 |
0.015 |
10967.145 |
| DEMetro_Z |
30 |
170.473 |
0.025 |
0.013 |
13017.017 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.086 |
0.0465 |
1.086 |
| HMC |
5 |
2.873 |
0.00853 |
2.001 |
| HMC |
10 |
5.268 |
3.11e-05 |
5.050 |
| HMC |
15 |
5.720 |
8.87e-06 |
4.476 |
| HMC |
30 |
5.684 |
1.54e-05 |
9.382 |
| SMC |
2 |
-0.339 |
0.737 |
-0.124 |
| SMC |
5 |
0.339 |
0.737 |
0.123 |
| SMC |
10 |
2.474 |
0.0181 |
0.867 |
| SMC |
15 |
0.229 |
0.82 |
0.077 |
| SMC |
30 |
-1.414 |
0.166 |
-0.393 |
| Metro |
2 |
6.403 |
2.31e-06 |
6.151 |
| Metro |
5 |
7.525 |
3.95e-07 |
30.896 |
| Metro |
10 |
5.712 |
1.64e-05 |
32.081 |
| Metro |
15 |
5.880 |
1.15e-05 |
37.554 |
| Metro |
30 |
5.840 |
1.25e-05 |
40.175 |
| DEMetro_Z |
2 |
4.451 |
0.000151 |
2.603 |
| DEMetro_Z |
5 |
13.675 |
2.77e-11 |
1477.212 |
| DEMetro_Z |
10 |
32.791 |
3.44e-18 |
1822.046 |
| DEMetro_Z |
15 |
41.209 |
4.74e-20 |
1708.885 |
| DEMetro_Z |
30 |
68.535 |
3.18e-24 |
1500.886 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
3.019
|
0.00706
|
0.675
|
| Metro_vs_DEMetro_Z |
1
|
-13.384
|
4.01e-11
|
-2.993
|
| Metro_vs_DEMetro_Z |
2
|
-32.416
|
4.27e-18
|
-7.248
|
| Metro_vs_DEMetro_Z |
3
|
-40.061
|
8.07e-20
|
-8.958
|
| Metro_vs_DEMetro_Z |
4
|
-60.892
|
3.01e-23
|
-13.616
|
| DEMetro_Z_vs_SMC |
0
|
4.281
|
0.000403
|
0.957
|
| DEMetro_Z_vs_SMC |
1
|
13.684
|
2.74e-11
|
3.060
|
| DEMetro_Z_vs_SMC |
2
|
32.702
|
3.62e-18
|
7.312
|
| DEMetro_Z_vs_SMC |
3
|
41.307
|
4.54e-20
|
9.237
|
| DEMetro_Z_vs_SMC |
4
|
68.629
|
3.13e-24
|
15.346
|
| HMC_vs_DEMetro_Z |
0
|
-2.215
|
0.0392
|
-0.495
|
| HMC_vs_DEMetro_Z |
1
|
-13.656
|
2.84e-11
|
-3.053
|
| HMC_vs_DEMetro_Z |
2
|
-32.711
|
3.6e-18
|
-7.314
|
| HMC_vs_DEMetro_Z |
3
|
-41.213
|
4.74e-20
|
-9.216
|
| HMC_vs_DEMetro_Z |
4
|
-69.649
|
2.37e-24
|
-15.574
|
| HMC_vs_Metro |
0
|
-5.015
|
7.69e-05
|
-1.121
|
| HMC_vs_Metro |
1
|
-6.884
|
1.45e-06
|
-1.539
|
| HMC_vs_Metro |
2
|
-4.714
|
0.000151
|
-1.054
|
| HMC_vs_Metro |
3
|
-5.035
|
7.35e-05
|
-1.126
|
| HMC_vs_Metro |
4
|
-4.299
|
0.000387
|
-0.961
|
| HMC_vs_SMC |
0
|
2.009
|
0.0589
|
0.449
|
| HMC_vs_SMC |
1
|
2.902
|
0.00914
|
0.649
|
| HMC_vs_SMC |
2
|
4.389
|
0.000316
|
0.981
|
| HMC_vs_SMC |
3
|
5.370
|
3.51e-05
|
1.201
|
| HMC_vs_SMC |
4
|
5.870
|
1.18e-05
|
1.313
|
| Metro_vs_SMC |
0
|
6.520
|
3.03e-06
|
1.458
|
| Metro_vs_SMC |
1
|
7.485
|
4.44e-07
|
1.674
|
| Metro_vs_SMC |
2
|
5.621
|
2.02e-05
|
1.257
|
| Metro_vs_SMC |
3
|
5.925
|
1.05e-05
|
1.325
|
| Metro_vs_SMC |
4
|
5.920
|
1.06e-05
|
1.324
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.038 |
0.029 |
0.008 |
1.086 |
| HMC |
5 |
0.037 |
0.025 |
0.006 |
2.001 |
| HMC |
10 |
0.049 |
0.022 |
0.005 |
5.050 |
| HMC |
15 |
0.050 |
0.024 |
0.006 |
4.476 |
| HMC |
30 |
0.091 |
0.026 |
0.007 |
9.382 |
| SMC |
2 |
0.028 |
0.029 |
0.008 |
-0.124 |
| SMC |
5 |
0.025 |
0.025 |
0.006 |
0.123 |
| SMC |
10 |
0.027 |
0.022 |
0.005 |
0.867 |
| SMC |
15 |
0.025 |
0.024 |
0.006 |
0.077 |
| SMC |
30 |
0.023 |
0.026 |
0.007 |
-0.393 |
| Metro |
2 |
0.080 |
0.029 |
0.008 |
6.151 |
| Metro |
5 |
0.220 |
0.025 |
0.006 |
30.896 |
| Metro |
10 |
0.191 |
0.022 |
0.005 |
32.081 |
| Metro |
15 |
0.243 |
0.024 |
0.006 |
37.554 |
| Metro |
30 |
0.304 |
0.026 |
0.007 |
40.175 |
| DEMetro_Z |
2 |
0.050 |
0.029 |
0.008 |
2.603 |
| DEMetro_Z |
5 |
9.391 |
0.025 |
0.006 |
1477.212 |
| DEMetro_Z |
10 |
9.632 |
0.022 |
0.005 |
1822.046 |
| DEMetro_Z |
15 |
9.963 |
0.024 |
0.006 |
1708.885 |
| DEMetro_Z |
30 |
10.431 |
0.026 |
0.007 |
1500.886 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.485 |
0.148 |
0.689 |
| HMC |
5 |
3.188 |
0.00373 |
1.805 |
| HMC |
10 |
5.059 |
5.12e-05 |
4.887 |
| HMC |
15 |
6.228 |
1.65e-06 |
3.749 |
| HMC |
30 |
5.877 |
9.55e-06 |
8.320 |
| SMC |
2 |
-1.024 |
0.312 |
-0.328 |
| SMC |
5 |
0.525 |
0.603 |
0.188 |
| SMC |
10 |
2.012 |
0.052 |
0.762 |
| SMC |
15 |
0.250 |
0.804 |
0.080 |
| SMC |
30 |
-0.930 |
0.358 |
-0.288 |
| Metro |
2 |
6.796 |
8.42e-07 |
5.846 |
| Metro |
5 |
7.896 |
1.87e-07 |
22.498 |
| Metro |
10 |
5.878 |
1.15e-05 |
32.009 |
| Metro |
15 |
6.074 |
7.55e-06 |
30.466 |
| Metro |
30 |
7.891 |
1.99e-07 |
36.478 |
| DEMetro_Z |
2 |
3.877 |
0.000659 |
2.233 |
| DEMetro_Z |
5 |
33.619 |
1.88e-18 |
156.684 |
| DEMetro_Z |
10 |
39.522 |
8.87e-20 |
179.646 |
| DEMetro_Z |
15 |
77.349 |
6.22e-26 |
129.445 |
| DEMetro_Z |
30 |
70.206 |
4.83e-25 |
123.378 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.285
|
0.0004
|
0.958
|
| DEMetro_Z_vs_SMC |
1
|
33.939
|
1.81e-18
|
7.589
|
| DEMetro_Z_vs_SMC |
2
|
39.585
|
1.01e-19
|
8.851
|
| DEMetro_Z_vs_SMC |
3
|
74.565
|
6.51e-25
|
16.673
|
| DEMetro_Z_vs_SMC |
4
|
70.595
|
1.83e-24
|
15.785
|
| HMC_vs_Metro |
0
|
-6.012
|
8.75e-06
|
-1.344
|
| HMC_vs_Metro |
1
|
-6.861
|
1.52e-06
|
-1.534
|
| HMC_vs_Metro |
2
|
-4.832
|
0.000116
|
-1.081
|
| HMC_vs_Metro |
3
|
-5.223
|
4.84e-05
|
-1.168
|
| HMC_vs_Metro |
4
|
-5.887
|
1.14e-05
|
-1.316
|
| Metro_vs_DEMetro_Z |
0
|
3.557
|
0.0021
|
0.795
|
| Metro_vs_DEMetro_Z |
1
|
-25.085
|
5e-16
|
-5.609
|
| Metro_vs_DEMetro_Z |
2
|
-25.958
|
2.66e-16
|
-5.804
|
| Metro_vs_DEMetro_Z |
3
|
-18.386
|
1.46e-13
|
-4.111
|
| Metro_vs_DEMetro_Z |
4
|
-15.927
|
1.91e-12
|
-3.561
|
| HMC_vs_SMC |
0
|
2.026
|
0.0571
|
0.453
|
| HMC_vs_SMC |
1
|
3.028
|
0.00692
|
0.677
|
| HMC_vs_SMC |
2
|
4.565
|
0.000211
|
1.021
|
| HMC_vs_SMC |
3
|
5.989
|
9.2e-06
|
1.339
|
| HMC_vs_SMC |
4
|
5.999
|
8.99e-06
|
1.341
|
| Metro_vs_SMC |
0
|
6.929
|
1.32e-06
|
1.549
|
| Metro_vs_SMC |
1
|
7.787
|
2.5e-07
|
1.741
|
| Metro_vs_SMC |
2
|
5.813
|
1.34e-05
|
1.300
|
| Metro_vs_SMC |
3
|
6.118
|
6.99e-06
|
1.368
|
| Metro_vs_SMC |
4
|
7.925
|
1.93e-07
|
1.772
|
| HMC_vs_DEMetro_Z |
0
|
-2.176
|
0.0424
|
-0.486
|
| HMC_vs_DEMetro_Z |
1
|
-33.491
|
2.32e-18
|
-7.489
|
| HMC_vs_DEMetro_Z |
2
|
-36.291
|
5.16e-19
|
-8.115
|
| HMC_vs_DEMetro_Z |
3
|
-67.311
|
4.52e-24
|
-15.051
|
| HMC_vs_DEMetro_Z |
4
|
-45.772
|
6.58e-21
|
-10.235
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.019 |
0.015 |
0.005 |
0.689 |
| HMC |
5 |
0.022 |
0.013 |
0.005 |
1.805 |
| HMC |
10 |
0.028 |
0.012 |
0.003 |
4.887 |
| HMC |
15 |
0.030 |
0.014 |
0.004 |
3.749 |
| HMC |
30 |
0.053 |
0.015 |
0.005 |
8.320 |
| SMC |
2 |
0.014 |
0.015 |
0.005 |
-0.328 |
| SMC |
5 |
0.014 |
0.013 |
0.005 |
0.188 |
| SMC |
10 |
0.014 |
0.012 |
0.003 |
0.762 |
| SMC |
15 |
0.014 |
0.014 |
0.004 |
0.080 |
| SMC |
30 |
0.014 |
0.015 |
0.005 |
-0.288 |
| Metro |
2 |
0.044 |
0.015 |
0.005 |
5.846 |
| Metro |
5 |
0.122 |
0.013 |
0.005 |
22.498 |
| Metro |
10 |
0.120 |
0.012 |
0.003 |
32.009 |
| Metro |
15 |
0.148 |
0.014 |
0.004 |
30.466 |
| Metro |
30 |
0.182 |
0.015 |
0.005 |
36.478 |
| DEMetro_Z |
2 |
0.026 |
0.015 |
0.005 |
2.233 |
| DEMetro_Z |
5 |
0.770 |
0.013 |
0.005 |
156.684 |
| DEMetro_Z |
10 |
0.620 |
0.012 |
0.003 |
179.646 |
| DEMetro_Z |
15 |
0.582 |
0.014 |
0.004 |
129.445 |
| DEMetro_Z |
30 |
0.581 |
0.015 |
0.005 |
123.378 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.360 |
0.721 |
0.144 |
| HMC |
5 |
2.317 |
0.0294 |
1.513 |
| HMC |
10 |
3.164 |
0.00439 |
2.389 |
| HMC |
15 |
3.521 |
0.00196 |
3.066 |
| HMC |
30 |
6.014 |
5.44e-06 |
5.668 |
| SMC |
2 |
0.330 |
0.744 |
0.117 |
| SMC |
5 |
0.009 |
0.993 |
0.003 |
| SMC |
10 |
0.716 |
0.478 |
0.241 |
| SMC |
15 |
0.088 |
0.931 |
0.031 |
| SMC |
30 |
-2.003 |
0.0539 |
-0.522 |
| Metro |
2 |
4.994 |
5.79e-05 |
4.598 |
| Metro |
5 |
6.198 |
5.44e-06 |
14.256 |
| Metro |
10 |
5.056 |
6.86e-05 |
18.420 |
| Metro |
15 |
7.136 |
8.52e-07 |
33.000 |
| Metro |
30 |
10.013 |
4.63e-09 |
30.448 |
| DEMetro_Z |
2 |
2.359 |
0.0263 |
1.381 |
| DEMetro_Z |
5 |
4.055 |
0.000676 |
320.043 |
| DEMetro_Z |
10 |
11.741 |
3.74e-10 |
807.819 |
| DEMetro_Z |
15 |
22.906 |
2.66e-15 |
945.326 |
| DEMetro_Z |
30 |
38.969 |
1.35e-19 |
915.814 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.157
|
0.044
|
-0.482
|
| HMC_vs_DEMetro_Z |
1
|
-4.035
|
0.000707
|
-0.902
|
| HMC_vs_DEMetro_Z |
2
|
-11.691
|
4.02e-10
|
-2.614
|
| HMC_vs_DEMetro_Z |
3
|
-23.006
|
2.46e-15
|
-5.144
|
| HMC_vs_DEMetro_Z |
4
|
-38.568
|
1.65e-19
|
-8.624
|
| Metro_vs_SMC |
0
|
5.388
|
3.37e-05
|
1.205
|
| Metro_vs_SMC |
1
|
6.483
|
3.27e-06
|
1.450
|
| Metro_vs_SMC |
2
|
5.180
|
5.33e-05
|
1.158
|
| Metro_vs_SMC |
3
|
7.204
|
7.66e-07
|
1.611
|
| Metro_vs_SMC |
4
|
10.189
|
3.89e-09
|
2.278
|
| Metro_vs_DEMetro_Z |
0
|
3.016
|
0.0071
|
0.674
|
| Metro_vs_DEMetro_Z |
1
|
-3.941
|
0.000877
|
-0.881
|
| Metro_vs_DEMetro_Z |
2
|
-11.573
|
4.77e-10
|
-2.588
|
| Metro_vs_DEMetro_Z |
3
|
-21.454
|
8.86e-15
|
-4.797
|
| Metro_vs_DEMetro_Z |
4
|
-38.132
|
2.04e-19
|
-8.526
|
| HMC_vs_Metro |
0
|
-4.585
|
0.000202
|
-1.025
|
| HMC_vs_Metro |
1
|
-5.972
|
9.53e-06
|
-1.335
|
| HMC_vs_Metro |
2
|
-4.701
|
0.000155
|
-1.051
|
| HMC_vs_Metro |
3
|
-5.864
|
1.2e-05
|
-1.311
|
| HMC_vs_Metro |
4
|
-7.440
|
4.84e-07
|
-1.664
|
| HMC_vs_SMC |
0
|
0.061
|
0.952
|
0.014
|
| HMC_vs_SMC |
1
|
2.312
|
0.0321
|
0.517
|
| HMC_vs_SMC |
2
|
3.270
|
0.00403
|
0.731
|
| HMC_vs_SMC |
3
|
3.384
|
0.00311
|
0.757
|
| HMC_vs_SMC |
4
|
6.526
|
2.99e-06
|
1.459
|
| DEMetro_Z_vs_SMC |
0
|
2.237
|
0.0375
|
0.500
|
| DEMetro_Z_vs_SMC |
1
|
4.055
|
0.000676
|
0.907
|
| DEMetro_Z_vs_SMC |
2
|
11.728
|
3.81e-10
|
2.622
|
| DEMetro_Z_vs_SMC |
3
|
22.933
|
2.61e-15
|
5.128
|
| DEMetro_Z_vs_SMC |
4
|
38.997
|
1.34e-19
|
8.720
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.024 |
0.022 |
0.013 |
0.144 |
| HMC |
5 |
0.035 |
0.019 |
0.011 |
1.513 |
| HMC |
10 |
0.040 |
0.016 |
0.010 |
2.389 |
| HMC |
15 |
0.054 |
0.020 |
0.011 |
3.066 |
| HMC |
30 |
0.096 |
0.022 |
0.013 |
5.668 |
| SMC |
2 |
0.024 |
0.022 |
0.013 |
0.117 |
| SMC |
5 |
0.019 |
0.019 |
0.011 |
0.003 |
| SMC |
10 |
0.019 |
0.016 |
0.010 |
0.241 |
| SMC |
15 |
0.021 |
0.020 |
0.011 |
0.031 |
| SMC |
30 |
0.016 |
0.022 |
0.013 |
-0.522 |
| Metro |
2 |
0.081 |
0.022 |
0.013 |
4.598 |
| Metro |
5 |
0.173 |
0.019 |
0.011 |
14.256 |
| Metro |
10 |
0.200 |
0.016 |
0.010 |
18.420 |
| Metro |
15 |
0.380 |
0.020 |
0.011 |
33.000 |
| Metro |
30 |
0.419 |
0.022 |
0.013 |
30.448 |
| DEMetro_Z |
2 |
0.040 |
0.022 |
0.013 |
1.381 |
| DEMetro_Z |
5 |
3.466 |
0.019 |
0.011 |
320.043 |
| DEMetro_Z |
10 |
8.054 |
0.016 |
0.010 |
807.819 |
| DEMetro_Z |
15 |
10.317 |
0.020 |
0.011 |
945.326 |
| DEMetro_Z |
30 |
11.953 |
0.022 |
0.013 |
915.814 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.185 |
0.00422 |
2.481 |
| HMC |
5 |
3.585 |
0.00178 |
3.933 |
| HMC |
10 |
4.556 |
0.000177 |
4.882 |
| HMC |
15 |
4.450 |
0.000186 |
3.277 |
| HMC |
30 |
3.977 |
0.000706 |
4.361 |
| SMC |
2 |
0.804 |
0.427 |
0.291 |
| SMC |
5 |
1.406 |
0.169 |
0.528 |
| SMC |
10 |
1.855 |
0.0738 |
0.880 |
| SMC |
15 |
1.770 |
0.0847 |
0.573 |
| SMC |
30 |
1.303 |
0.201 |
0.490 |
| Metro |
2 |
4.672 |
0.000133 |
4.860 |
| Metro |
5 |
5.278 |
4.1e-05 |
13.952 |
| Metro |
10 |
5.071 |
6.71e-05 |
27.228 |
| Metro |
15 |
6.213 |
5.41e-06 |
17.319 |
| Metro |
30 |
8.241 |
9.75e-08 |
22.585 |
| DEMetro_Z |
2 |
5.135 |
3.38e-05 |
3.741 |
| DEMetro_Z |
5 |
3.276 |
0.00397 |
2493.668 |
| DEMetro_Z |
10 |
7.651 |
3.23e-07 |
2479.958 |
| DEMetro_Z |
15 |
7.710 |
2.89e-07 |
1681.457 |
| DEMetro_Z |
30 |
9.113 |
2.3e-08 |
1654.760 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.192
|
0.00479
|
0.714
|
| HMC_vs_SMC |
1
|
3.300
|
0.00376
|
0.738
|
| HMC_vs_SMC |
2
|
3.587
|
0.00197
|
0.802
|
| HMC_vs_SMC |
3
|
4.240
|
0.000443
|
0.948
|
| HMC_vs_SMC |
4
|
3.421
|
0.00286
|
0.765
|
| Metro_vs_DEMetro_Z |
0
|
0.804
|
0.432
|
0.180
|
| Metro_vs_DEMetro_Z |
1
|
-3.259
|
0.00413
|
-0.729
|
| Metro_vs_DEMetro_Z |
2
|
-7.575
|
3.73e-07
|
-1.694
|
| Metro_vs_DEMetro_Z |
3
|
-7.662
|
3.16e-07
|
-1.713
|
| Metro_vs_DEMetro_Z |
4
|
-8.969
|
2.94e-08
|
-2.006
|
| HMC_vs_Metro |
0
|
-1.974
|
0.0631
|
-0.441
|
| HMC_vs_Metro |
1
|
-4.067
|
0.000658
|
-0.909
|
| HMC_vs_Metro |
2
|
-4.703
|
0.000155
|
-1.052
|
| HMC_vs_Metro |
3
|
-5.165
|
5.51e-05
|
-1.155
|
| HMC_vs_Metro |
4
|
-5.818
|
1.32e-05
|
-1.301
|
| HMC_vs_DEMetro_Z |
0
|
-1.126
|
0.274
|
-0.252
|
| HMC_vs_DEMetro_Z |
1
|
-3.270
|
0.00403
|
-0.731
|
| HMC_vs_DEMetro_Z |
2
|
-7.643
|
3.28e-07
|
-1.709
|
| HMC_vs_DEMetro_Z |
3
|
-7.692
|
2.99e-07
|
-1.720
|
| HMC_vs_DEMetro_Z |
4
|
-9.096
|
2.37e-08
|
-2.034
|
| Metro_vs_SMC |
0
|
4.115
|
0.000589
|
0.920
|
| Metro_vs_SMC |
1
|
5.220
|
4.88e-05
|
1.167
|
| Metro_vs_SMC |
2
|
4.834
|
0.000115
|
1.081
|
| Metro_vs_SMC |
3
|
5.944
|
1.01e-05
|
1.329
|
| Metro_vs_SMC |
4
|
7.822
|
2.34e-07
|
1.749
|
| DEMetro_Z_vs_SMC |
0
|
4.418
|
0.000295
|
0.988
|
| DEMetro_Z_vs_SMC |
1
|
3.275
|
0.00398
|
0.732
|
| DEMetro_Z_vs_SMC |
2
|
7.647
|
3.26e-07
|
1.710
|
| DEMetro_Z_vs_SMC |
3
|
7.709
|
2.89e-07
|
1.724
|
| DEMetro_Z_vs_SMC |
4
|
9.109
|
2.31e-08
|
2.037
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.045 |
0.019 |
0.010 |
2.481 |
| HMC |
5 |
0.057 |
0.022 |
0.009 |
3.933 |
| HMC |
10 |
0.068 |
0.024 |
0.009 |
4.882 |
| HMC |
15 |
0.072 |
0.024 |
0.015 |
3.277 |
| HMC |
30 |
0.082 |
0.025 |
0.013 |
4.361 |
| SMC |
2 |
0.023 |
0.019 |
0.010 |
0.291 |
| SMC |
5 |
0.027 |
0.022 |
0.009 |
0.528 |
| SMC |
10 |
0.032 |
0.024 |
0.009 |
0.880 |
| SMC |
15 |
0.033 |
0.024 |
0.015 |
0.573 |
| SMC |
30 |
0.032 |
0.025 |
0.013 |
0.490 |
| Metro |
2 |
0.070 |
0.019 |
0.010 |
4.860 |
| Metro |
5 |
0.147 |
0.022 |
0.009 |
13.952 |
| Metro |
10 |
0.266 |
0.024 |
0.009 |
27.228 |
| Metro |
15 |
0.279 |
0.024 |
0.015 |
17.319 |
| Metro |
30 |
0.321 |
0.025 |
0.013 |
22.585 |
| DEMetro_Z |
2 |
0.058 |
0.019 |
0.010 |
3.741 |
| DEMetro_Z |
5 |
22.394 |
0.022 |
0.009 |
2493.668 |
| DEMetro_Z |
10 |
22.007 |
0.024 |
0.009 |
2479.958 |
| DEMetro_Z |
15 |
24.811 |
0.024 |
0.015 |
1681.457 |
| DEMetro_Z |
30 |
21.693 |
0.025 |
0.013 |
1654.760 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.264 |
0.0305 |
0.958 |
| HMC |
5 |
3.937 |
0.000678 |
3.011 |
| HMC |
10 |
5.612 |
1.2e-05 |
4.566 |
| HMC |
15 |
5.325 |
3e-05 |
6.016 |
| HMC |
30 |
7.162 |
5.91e-07 |
9.367 |
| SMC |
2 |
-0.289 |
0.775 |
-0.112 |
| SMC |
5 |
0.453 |
0.653 |
0.154 |
| SMC |
10 |
1.512 |
0.139 |
0.564 |
| SMC |
15 |
0.417 |
0.679 |
0.151 |
| SMC |
30 |
-1.271 |
0.212 |
-0.354 |
| Metro |
2 |
5.921 |
7.75e-06 |
6.710 |
| Metro |
5 |
7.552 |
3.6e-07 |
21.438 |
| Metro |
10 |
6.998 |
1.13e-06 |
36.087 |
| Metro |
15 |
8.408 |
7.8e-08 |
53.470 |
| Metro |
30 |
10.691 |
1.68e-09 |
47.666 |
| DEMetro_Z |
2 |
4.930 |
4.67e-05 |
3.056 |
| DEMetro_Z |
5 |
4.246 |
0.000437 |
492.977 |
| DEMetro_Z |
10 |
12.675 |
1.02e-10 |
1334.695 |
| DEMetro_Z |
15 |
25.487 |
3.73e-16 |
1522.062 |
| DEMetro_Z |
30 |
38.822 |
1.45e-19 |
1416.972 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
2.728
|
0.0134
|
0.610
|
| Metro_vs_DEMetro_Z |
1
|
-4.123
|
0.000579
|
-0.922
|
| Metro_vs_DEMetro_Z |
2
|
-12.368
|
1.55e-10
|
-2.765
|
| Metro_vs_DEMetro_Z |
3
|
-23.702
|
1.42e-15
|
-5.300
|
| Metro_vs_DEMetro_Z |
4
|
-37.905
|
2.28e-19
|
-8.476
|
| DEMetro_Z_vs_SMC |
0
|
5.068
|
6.83e-05
|
1.133
|
| DEMetro_Z_vs_SMC |
1
|
4.243
|
0.00044
|
0.949
|
| DEMetro_Z_vs_SMC |
2
|
12.668
|
1.03e-10
|
2.833
|
| DEMetro_Z_vs_SMC |
3
|
25.504
|
3.68e-16
|
5.703
|
| DEMetro_Z_vs_SMC |
4
|
38.836
|
1.45e-19
|
8.684
|
| HMC_vs_DEMetro_Z |
0
|
-3.464
|
0.0026
|
-0.774
|
| HMC_vs_DEMetro_Z |
1
|
-4.218
|
0.000465
|
-0.943
|
| HMC_vs_DEMetro_Z |
2
|
-12.621
|
1.1e-10
|
-2.822
|
| HMC_vs_DEMetro_Z |
3
|
-25.527
|
3.62e-16
|
-5.708
|
| HMC_vs_DEMetro_Z |
4
|
-38.562
|
1.65e-19
|
-8.623
|
| HMC_vs_Metro |
0
|
-4.729
|
0.000146
|
-1.057
|
| HMC_vs_Metro |
1
|
-6.824
|
1.63e-06
|
-1.526
|
| HMC_vs_Metro |
2
|
-6.269
|
5.09e-06
|
-1.402
|
| HMC_vs_Metro |
3
|
-6.960
|
1.24e-06
|
-1.556
|
| HMC_vs_Metro |
4
|
-7.919
|
1.95e-07
|
-1.771
|
| HMC_vs_SMC |
0
|
2.066
|
0.0527
|
0.462
|
| HMC_vs_SMC |
1
|
4.123
|
0.000579
|
0.922
|
| HMC_vs_SMC |
2
|
4.991
|
8.1e-05
|
1.116
|
| HMC_vs_SMC |
3
|
5.428
|
3.09e-05
|
1.214
|
| HMC_vs_SMC |
4
|
7.534
|
4.04e-07
|
1.685
|
| Metro_vs_SMC |
0
|
6.564
|
2.77e-06
|
1.468
|
| Metro_vs_SMC |
1
|
7.805
|
2.41e-07
|
1.745
|
| Metro_vs_SMC |
2
|
7.039
|
1.06e-06
|
1.574
|
| Metro_vs_SMC |
3
|
8.420
|
7.77e-08
|
1.883
|
| Metro_vs_SMC |
4
|
10.844
|
1.41e-09
|
2.425
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.037 |
0.029 |
0.008 |
0.958 |
| HMC |
5 |
0.044 |
0.025 |
0.006 |
3.011 |
| HMC |
10 |
0.046 |
0.022 |
0.005 |
4.566 |
| HMC |
15 |
0.059 |
0.024 |
0.006 |
6.016 |
| HMC |
30 |
0.091 |
0.026 |
0.007 |
9.367 |
| SMC |
2 |
0.028 |
0.029 |
0.008 |
-0.112 |
| SMC |
5 |
0.025 |
0.025 |
0.006 |
0.154 |
| SMC |
10 |
0.025 |
0.022 |
0.005 |
0.564 |
| SMC |
15 |
0.025 |
0.024 |
0.006 |
0.151 |
| SMC |
30 |
0.023 |
0.026 |
0.007 |
-0.354 |
| Metro |
2 |
0.084 |
0.029 |
0.008 |
6.710 |
| Metro |
5 |
0.160 |
0.025 |
0.006 |
21.438 |
| Metro |
10 |
0.213 |
0.022 |
0.005 |
36.087 |
| Metro |
15 |
0.335 |
0.024 |
0.006 |
53.470 |
| Metro |
30 |
0.356 |
0.026 |
0.007 |
47.666 |
| DEMetro_Z |
2 |
0.054 |
0.029 |
0.008 |
3.056 |
| DEMetro_Z |
5 |
3.150 |
0.025 |
0.006 |
492.977 |
| DEMetro_Z |
10 |
7.062 |
0.022 |
0.005 |
1334.695 |
| DEMetro_Z |
15 |
8.877 |
0.024 |
0.006 |
1522.062 |
| DEMetro_Z |
30 |
9.849 |
0.026 |
0.007 |
1416.972 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.598 |
0.0135 |
0.933 |
| HMC |
5 |
4.102 |
0.000401 |
2.612 |
| HMC |
10 |
5.192 |
3.59e-05 |
4.733 |
| HMC |
15 |
5.768 |
9.25e-06 |
5.229 |
| HMC |
30 |
7.589 |
2.36e-07 |
9.307 |
| SMC |
2 |
-1.037 |
0.307 |
-0.366 |
| SMC |
5 |
0.550 |
0.586 |
0.163 |
| SMC |
10 |
1.353 |
0.186 |
0.559 |
| SMC |
15 |
0.698 |
0.49 |
0.246 |
| SMC |
30 |
-0.361 |
0.72 |
-0.118 |
| Metro |
2 |
5.203 |
4.04e-05 |
6.106 |
| Metro |
5 |
8.120 |
1.14e-07 |
16.912 |
| Metro |
10 |
9.339 |
1.47e-08 |
35.725 |
| Metro |
15 |
8.481 |
6.76e-08 |
43.297 |
| Metro |
30 |
12.584 |
1.05e-10 |
46.150 |
| DEMetro_Z |
2 |
4.708 |
7.19e-05 |
2.612 |
| DEMetro_Z |
5 |
10.577 |
2.1e-09 |
108.957 |
| DEMetro_Z |
10 |
47.279 |
3.16e-21 |
257.915 |
| DEMetro_Z |
15 |
80.704 |
7.07e-26 |
205.642 |
| DEMetro_Z |
30 |
57.686 |
6.11e-23 |
206.492 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.341
|
3.73e-05
|
1.194
|
| DEMetro_Z_vs_SMC |
1
|
10.578
|
2.11e-09
|
2.365
|
| DEMetro_Z_vs_SMC |
2
|
47.819
|
2.88e-21
|
10.693
|
| DEMetro_Z_vs_SMC |
3
|
84.984
|
5.46e-26
|
19.003
|
| DEMetro_Z_vs_SMC |
4
|
58.754
|
5.91e-23
|
13.138
|
| HMC_vs_Metro |
0
|
-4.275
|
0.000409
|
-0.956
|
| HMC_vs_Metro |
1
|
-7.254
|
6.94e-07
|
-1.622
|
| HMC_vs_Metro |
2
|
-8.037
|
1.56e-07
|
-1.797
|
| HMC_vs_Metro |
3
|
-7.103
|
9.35e-07
|
-1.588
|
| HMC_vs_Metro |
4
|
-8.836
|
3.71e-08
|
-1.976
|
| Metro_vs_DEMetro_Z |
0
|
2.460
|
0.0236
|
0.550
|
| Metro_vs_DEMetro_Z |
1
|
-9.725
|
8.24e-09
|
-2.175
|
| Metro_vs_DEMetro_Z |
2
|
-34.839
|
1.11e-18
|
-7.790
|
| Metro_vs_DEMetro_Z |
3
|
-25.733
|
3.12e-16
|
-5.754
|
| Metro_vs_DEMetro_Z |
4
|
-35.007
|
1.01e-18
|
-7.828
|
| HMC_vs_SMC |
0
|
3.227
|
0.00444
|
0.722
|
| HMC_vs_SMC |
1
|
4.321
|
0.000368
|
0.966
|
| HMC_vs_SMC |
2
|
4.494
|
0.000248
|
1.005
|
| HMC_vs_SMC |
3
|
6.313
|
4.65e-06
|
1.412
|
| HMC_vs_SMC |
4
|
7.617
|
3.45e-07
|
1.703
|
| Metro_vs_SMC |
0
|
5.897
|
1.12e-05
|
1.319
|
| Metro_vs_SMC |
1
|
8.053
|
1.52e-07
|
1.801
|
| Metro_vs_SMC |
2
|
9.397
|
1.42e-08
|
2.101
|
| Metro_vs_SMC |
3
|
8.354
|
8.76e-08
|
1.868
|
| Metro_vs_SMC |
4
|
12.678
|
1.02e-10
|
2.835
|
| HMC_vs_DEMetro_Z |
0
|
-3.330
|
0.00352
|
-0.745
|
| HMC_vs_DEMetro_Z |
1
|
-10.338
|
3.07e-09
|
-2.312
|
| HMC_vs_DEMetro_Z |
2
|
-42.276
|
2.94e-20
|
-9.453
|
| HMC_vs_DEMetro_Z |
3
|
-79.147
|
2.1e-25
|
-17.698
|
| HMC_vs_DEMetro_Z |
4
|
-49.474
|
1.52e-21
|
-11.063
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.020 |
0.015 |
0.005 |
0.933 |
| HMC |
5 |
0.026 |
0.013 |
0.005 |
2.612 |
| HMC |
10 |
0.028 |
0.012 |
0.003 |
4.733 |
| HMC |
15 |
0.037 |
0.014 |
0.004 |
5.229 |
| HMC |
30 |
0.058 |
0.015 |
0.005 |
9.307 |
| SMC |
2 |
0.014 |
0.015 |
0.005 |
-0.366 |
| SMC |
5 |
0.014 |
0.013 |
0.005 |
0.163 |
| SMC |
10 |
0.014 |
0.012 |
0.003 |
0.559 |
| SMC |
15 |
0.015 |
0.014 |
0.004 |
0.246 |
| SMC |
30 |
0.014 |
0.015 |
0.005 |
-0.118 |
| Metro |
2 |
0.045 |
0.015 |
0.005 |
6.106 |
| Metro |
5 |
0.095 |
0.013 |
0.005 |
16.912 |
| Metro |
10 |
0.133 |
0.012 |
0.003 |
35.725 |
| Metro |
15 |
0.204 |
0.014 |
0.004 |
43.297 |
| Metro |
30 |
0.227 |
0.015 |
0.005 |
46.150 |
| DEMetro_Z |
2 |
0.028 |
0.015 |
0.005 |
2.612 |
| DEMetro_Z |
5 |
0.540 |
0.013 |
0.005 |
108.957 |
| DEMetro_Z |
10 |
0.886 |
0.012 |
0.003 |
257.915 |
| DEMetro_Z |
15 |
0.917 |
0.014 |
0.004 |
205.642 |
| DEMetro_Z |
30 |
0.963 |
0.015 |
0.005 |
206.492 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_heavy_Tails
(MvStudentT,
dimension,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.634 |
0.111 |
0.562 |
| HMC |
5 |
-2.370 |
0.0244 |
-0.609 |
| HMC |
10 |
-0.683 |
0.499 |
-0.200 |
| HMC |
15 |
1.805 |
0.0852 |
1.682 |
| HMC |
30 |
2.303 |
0.0327 |
15.082 |
| SMC |
2 |
3.253 |
0.0024 |
1.043 |
| SMC |
5 |
14.090 |
1.25e-11 |
32.987 |
| SMC |
10 |
10.375 |
1.48e-10 |
6.188 |
| SMC |
15 |
25.505 |
2.93e-16 |
84.604 |
| SMC |
30 |
72.503 |
1.01e-24 |
499.715 |
| Metro |
2 |
2.030 |
0.0498 |
0.745 |
| Metro |
5 |
4.400 |
0.000225 |
3.582 |
| Metro |
10 |
1.355 |
0.184 |
0.431 |
| Metro |
15 |
2.962 |
0.00796 |
11.124 |
| Metro |
30 |
3.804 |
0.0012 |
89.465 |
| DEMetro_Z |
2 |
3.511 |
0.00139 |
1.534 |
| DEMetro_Z |
5 |
7.131 |
8.84e-07 |
233.960 |
| DEMetro_Z |
10 |
5.264 |
4.37e-05 |
26.129 |
| DEMetro_Z |
15 |
19.522 |
4.9e-14 |
307.924 |
| DEMetro_Z |
30 |
23.829 |
1.29e-15 |
1805.514 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.115
|
0.0478
|
-0.473
|
| HMC_vs_DEMetro_Z |
1
|
-7.148
|
8.56e-07
|
-1.598
|
| HMC_vs_DEMetro_Z |
2
|
-5.416
|
3.16e-05
|
-1.211
|
| HMC_vs_DEMetro_Z |
3
|
-19.171
|
6.87e-14
|
-4.287
|
| HMC_vs_DEMetro_Z |
4
|
-23.933
|
1.19e-15
|
-5.352
|
| Metro_vs_SMC |
0
|
-0.802
|
0.432
|
-0.179
|
| Metro_vs_SMC |
1
|
-12.997
|
6.65e-11
|
-2.906
|
| Metro_vs_SMC |
2
|
-12.520
|
1.26e-10
|
-2.799
|
| Metro_vs_SMC |
3
|
-14.480
|
1.02e-11
|
-3.238
|
| Metro_vs_SMC |
4
|
-16.758
|
7.72e-13
|
-3.747
|
| Metro_vs_DEMetro_Z |
0
|
-1.414
|
0.174
|
-0.316
|
| Metro_vs_DEMetro_Z |
1
|
-7.009
|
1.13e-06
|
-1.567
|
| Metro_vs_DEMetro_Z |
2
|
-5.300
|
4.08e-05
|
-1.185
|
| Metro_vs_DEMetro_Z |
3
|
-18.792
|
9.86e-14
|
-4.202
|
| Metro_vs_DEMetro_Z |
4
|
-20.188
|
2.69e-14
|
-4.514
|
| HMC_vs_Metro |
0
|
-0.485
|
0.633
|
-0.108
|
| HMC_vs_Metro |
1
|
-5.713
|
1.66e-05
|
-1.278
|
| HMC_vs_Metro |
2
|
-2.175
|
0.0425
|
-0.486
|
| HMC_vs_Metro |
3
|
-2.363
|
0.0289
|
-0.528
|
| HMC_vs_Metro |
4
|
-3.001
|
0.00735
|
-0.671
|
| HMC_vs_SMC |
0
|
-1.169
|
0.257
|
-0.261
|
| HMC_vs_SMC |
1
|
-14.665
|
8.18e-12
|
-3.279
|
| HMC_vs_SMC |
2
|
-11.003
|
1.11e-09
|
-2.460
|
| HMC_vs_SMC |
3
|
-27.904
|
6.96e-17
|
-6.239
|
| HMC_vs_SMC |
4
|
-46.168
|
5.59e-21
|
-10.324
|
| DEMetro_Z_vs_SMC |
0
|
1.032
|
0.315
|
0.231
|
| DEMetro_Z_vs_SMC |
1
|
6.187
|
6.05e-06
|
1.383
|
| DEMetro_Z_vs_SMC |
2
|
4.157
|
0.000535
|
0.930
|
| DEMetro_Z_vs_SMC |
3
|
13.834
|
2.26e-11
|
3.093
|
| DEMetro_Z_vs_SMC |
4
|
17.362
|
4.1e-13
|
3.882
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.088 |
0.066 |
0.039 |
0.562 |
| HMC |
5 |
0.050 |
0.067 |
0.029 |
-0.609 |
| HMC |
10 |
0.077 |
0.095 |
0.090 |
-0.200 |
| HMC |
15 |
0.085 |
0.063 |
0.013 |
1.682 |
| HMC |
30 |
0.202 |
0.064 |
0.009 |
15.082 |
| SMC |
2 |
0.107 |
0.066 |
0.039 |
1.043 |
| SMC |
5 |
1.014 |
0.067 |
0.029 |
32.987 |
| SMC |
10 |
0.650 |
0.095 |
0.090 |
6.188 |
| SMC |
15 |
1.176 |
0.063 |
0.013 |
84.604 |
| SMC |
30 |
4.621 |
0.064 |
0.009 |
499.715 |
| Metro |
2 |
0.096 |
0.066 |
0.039 |
0.745 |
| Metro |
5 |
0.170 |
0.067 |
0.029 |
3.582 |
| Metro |
10 |
0.134 |
0.095 |
0.090 |
0.431 |
| Metro |
15 |
0.209 |
0.063 |
0.013 |
11.124 |
| Metro |
30 |
0.880 |
0.064 |
0.009 |
89.465 |
| DEMetro_Z |
2 |
0.127 |
0.066 |
0.039 |
1.534 |
| DEMetro_Z |
5 |
6.781 |
0.067 |
0.029 |
233.960 |
| DEMetro_Z |
10 |
2.438 |
0.095 |
0.090 |
26.129 |
| DEMetro_Z |
15 |
4.116 |
0.063 |
0.013 |
307.924 |
| DEMetro_Z |
30 |
16.528 |
0.064 |
0.009 |
1805.514 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.531 |
0.599 |
-0.142 |
| HMC |
5 |
-0.264 |
0.794 |
-0.065 |
| HMC |
10 |
-1.224 |
0.236 |
-0.274 |
| HMC |
15 |
0.726 |
0.472 |
0.237 |
| HMC |
30 |
1.390 |
0.18 |
2.208 |
| SMC |
2 |
0.671 |
0.508 |
0.162 |
| SMC |
5 |
22.793 |
1.8e-15 |
49.971 |
| SMC |
10 |
13.489 |
7.48e-12 |
3.100 |
| SMC |
15 |
61.035 |
2.09e-23 |
220.291 |
| SMC |
30 |
158.288 |
3.44e-31 |
922.805 |
| Metro |
2 |
-0.571 |
0.572 |
-0.149 |
| Metro |
5 |
-0.583 |
0.566 |
-0.135 |
| Metro |
10 |
-1.192 |
0.248 |
-0.267 |
| Metro |
15 |
1.093 |
0.288 |
4.322 |
| Metro |
30 |
1.673 |
0.111 |
52.068 |
| DEMetro_Z |
2 |
-0.558 |
0.581 |
-0.149 |
| DEMetro_Z |
5 |
5.148 |
5.71e-05 |
88.770 |
| DEMetro_Z |
10 |
1.756 |
0.0872 |
0.540 |
| DEMetro_Z |
15 |
10.013 |
4.92e-09 |
46.319 |
| DEMetro_Z |
30 |
19.679 |
4.26e-14 |
488.501 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-2.112
|
0.0482
|
-0.472
|
| HMC_vs_SMC |
1
|
-22.581
|
3.47e-15
|
-5.049
|
| HMC_vs_SMC |
2
|
-65.626
|
7.3e-24
|
-14.674
|
| HMC_vs_SMC |
3
|
-59.898
|
4.11e-23
|
-13.394
|
| HMC_vs_SMC |
4
|
-142.661
|
2.95e-30
|
-31.900
|
| Metro_vs_DEMetro_Z |
0
|
-0.020
|
0.984
|
-0.004
|
| Metro_vs_DEMetro_Z |
1
|
-5.153
|
5.65e-05
|
-1.152
|
| Metro_vs_DEMetro_Z |
2
|
-3.862
|
0.00105
|
-0.864
|
| Metro_vs_DEMetro_Z |
3
|
-8.148
|
1.27e-07
|
-1.822
|
| Metro_vs_DEMetro_Z |
4
|
-9.708
|
8.46e-09
|
-2.171
|
| HMC_vs_Metro |
0
|
0.104
|
0.918
|
0.023
|
| HMC_vs_Metro |
1
|
0.542
|
0.594
|
0.121
|
| HMC_vs_Metro |
2
|
-2.648
|
0.0159
|
-0.592
|
| HMC_vs_Metro |
3
|
-1.030
|
0.316
|
-0.230
|
| HMC_vs_Metro |
4
|
-1.601
|
0.126
|
-0.358
|
| HMC_vs_DEMetro_Z |
0
|
0.095
|
0.926
|
0.021
|
| HMC_vs_DEMetro_Z |
1
|
-5.167
|
5.49e-05
|
-1.155
|
| HMC_vs_DEMetro_Z |
2
|
-3.862
|
0.00105
|
-0.864
|
| HMC_vs_DEMetro_Z |
3
|
-9.939
|
5.81e-09
|
-2.222
|
| HMC_vs_DEMetro_Z |
4
|
-19.411
|
5.48e-14
|
-4.340
|
| Metro_vs_SMC |
0
|
-2.495
|
0.022
|
-0.558
|
| Metro_vs_SMC |
1
|
-22.991
|
2.49e-15
|
-5.141
|
| Metro_vs_SMC |
2
|
-65.913
|
6.72e-24
|
-14.739
|
| Metro_vs_SMC |
3
|
-46.264
|
5.38e-21
|
-10.345
|
| Metro_vs_SMC |
4
|
-27.014
|
1.27e-16
|
-6.041
|
| DEMetro_Z_vs_SMC |
0
|
-2.281
|
0.0343
|
-0.510
|
| DEMetro_Z_vs_SMC |
1
|
2.110
|
0.0483
|
0.472
|
| DEMetro_Z_vs_SMC |
2
|
-12.032
|
2.48e-10
|
-2.690
|
| DEMetro_Z_vs_SMC |
3
|
-32.647
|
3.74e-18
|
-7.300
|
| DEMetro_Z_vs_SMC |
4
|
-16.191
|
1.42e-12
|
-3.621
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
7.146 |
9.309 |
15.244 |
-0.142 |
| HMC |
5 |
8.322 |
9.700 |
21.181 |
-0.065 |
| HMC |
10 |
4.641 |
73.432 |
251.325 |
-0.274 |
| HMC |
15 |
9.576 |
7.127 |
10.327 |
0.237 |
| HMC |
30 |
25.392 |
6.949 |
8.351 |
2.208 |
| SMC |
2 |
11.774 |
9.309 |
15.244 |
0.162 |
| SMC |
5 |
1068.147 |
9.700 |
21.181 |
49.971 |
| SMC |
10 |
852.478 |
73.432 |
251.325 |
3.100 |
| SMC |
15 |
2282.080 |
7.127 |
10.327 |
220.291 |
| SMC |
30 |
7713.644 |
6.949 |
8.351 |
922.805 |
| Metro |
2 |
7.031 |
9.309 |
15.244 |
-0.149 |
| Metro |
5 |
6.849 |
9.700 |
21.181 |
-0.135 |
| Metro |
10 |
6.403 |
73.432 |
251.325 |
-0.267 |
| Metro |
15 |
51.763 |
7.127 |
10.327 |
4.322 |
| Metro |
30 |
441.787 |
6.949 |
8.351 |
52.068 |
| DEMetro_Z |
2 |
7.040 |
9.309 |
15.244 |
-0.149 |
| DEMetro_Z |
5 |
1889.968 |
9.700 |
21.181 |
88.770 |
| DEMetro_Z |
10 |
209.078 |
73.432 |
251.325 |
0.540 |
| DEMetro_Z |
15 |
485.461 |
7.127 |
10.327 |
46.319 |
| DEMetro_Z |
30 |
4086.605 |
6.949 |
8.351 |
488.501 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.310 |
0.0023 |
1.380 |
| HMC |
5 |
2.278 |
0.0331 |
2.070 |
| HMC |
10 |
1.556 |
0.129 |
0.635 |
| HMC |
15 |
5.296 |
3.7e-05 |
9.179 |
| HMC |
30 |
2.670 |
0.0151 |
47.942 |
| SMC |
2 |
10.172 |
2.73e-09 |
16.566 |
| SMC |
5 |
35.695 |
6.99e-19 |
788.805 |
| SMC |
10 |
102.575 |
6.95e-28 |
260.283 |
| SMC |
15 |
112.632 |
2.55e-28 |
1666.872 |
| SMC |
30 |
320.242 |
6.19e-37 |
6134.686 |
| Metro |
2 |
4.553 |
9.66e-05 |
2.311 |
| Metro |
5 |
5.070 |
6.17e-05 |
8.774 |
| Metro |
10 |
3.841 |
0.000717 |
2.185 |
| Metro |
15 |
2.002 |
0.0598 |
33.656 |
| Metro |
30 |
4.191 |
0.000495 |
510.175 |
| DEMetro_Z |
2 |
8.073 |
7.15e-09 |
3.885 |
| DEMetro_Z |
5 |
10.405 |
2.77e-09 |
604.387 |
| DEMetro_Z |
10 |
8.024 |
1.59e-07 |
83.393 |
| DEMetro_Z |
15 |
20.219 |
2.61e-14 |
665.509 |
| DEMetro_Z |
30 |
40.352 |
7.05e-20 |
4274.775 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.281
|
0.0342
|
-0.510
|
| Metro_vs_DEMetro_Z |
1
|
-10.189
|
3.89e-09
|
-2.278
|
| Metro_vs_DEMetro_Z |
2
|
-8.094
|
1.41e-07
|
-1.810
|
| Metro_vs_DEMetro_Z |
3
|
-19.645
|
4.41e-14
|
-4.393
|
| Metro_vs_DEMetro_Z |
4
|
-20.198
|
2.66e-14
|
-4.517
|
| DEMetro_Z_vs_SMC |
0
|
-7.195
|
7.8e-07
|
-1.609
|
| DEMetro_Z_vs_SMC |
1
|
-2.669
|
0.0152
|
-0.597
|
| DEMetro_Z_vs_SMC |
2
|
-16.553
|
9.61e-13
|
-3.701
|
| DEMetro_Z_vs_SMC |
3
|
-30.923
|
1.03e-17
|
-6.915
|
| DEMetro_Z_vs_SMC |
4
|
-16.491
|
1.03e-12
|
-3.687
|
| HMC_vs_DEMetro_Z |
0
|
-4.357
|
0.000339
|
-0.974
|
| HMC_vs_DEMetro_Z |
1
|
-10.376
|
2.9e-09
|
-2.320
|
| HMC_vs_DEMetro_Z |
2
|
-8.067
|
1.48e-07
|
-1.804
|
| HMC_vs_DEMetro_Z |
3
|
-20.106
|
2.89e-14
|
-4.496
|
| HMC_vs_DEMetro_Z |
4
|
-38.995
|
1.34e-19
|
-8.720
|
| HMC_vs_Metro |
0
|
-1.624
|
0.121
|
-0.363
|
| HMC_vs_Metro |
1
|
-3.523
|
0.00228
|
-0.788
|
| HMC_vs_Metro |
2
|
-3.654
|
0.00169
|
-0.817
|
| HMC_vs_Metro |
3
|
-1.544
|
0.139
|
-0.345
|
| HMC_vs_Metro |
4
|
-3.779
|
0.00127
|
-0.845
|
| HMC_vs_SMC |
0
|
-9.217
|
1.92e-08
|
-2.061
|
| HMC_vs_SMC |
1
|
-35.410
|
8.18e-19
|
-7.918
|
| HMC_vs_SMC |
2
|
-104.392
|
1.11e-27
|
-23.343
|
| HMC_vs_SMC |
3
|
-119.098
|
9.07e-29
|
-26.631
|
| HMC_vs_SMC |
4
|
-244.544
|
1.06e-34
|
-54.682
|
| Metro_vs_SMC |
0
|
-8.387
|
8.25e-08
|
-1.875
|
| Metro_vs_SMC |
1
|
-35.715
|
6.96e-19
|
-7.986
|
| Metro_vs_SMC |
2
|
-98.816
|
3.13e-27
|
-22.096
|
| Metro_vs_SMC |
3
|
-83.836
|
7.07e-26
|
-18.746
|
| Metro_vs_SMC |
4
|
-45.352
|
7.83e-21
|
-10.141
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.176 |
0.124 |
0.038 |
1.380 |
| HMC |
5 |
0.174 |
0.117 |
0.027 |
2.070 |
| HMC |
10 |
0.201 |
0.149 |
0.082 |
0.635 |
| HMC |
15 |
0.319 |
0.119 |
0.022 |
9.179 |
| HMC |
30 |
0.646 |
0.116 |
0.011 |
47.942 |
| SMC |
2 |
0.748 |
0.124 |
0.038 |
16.566 |
| SMC |
5 |
21.528 |
0.117 |
0.027 |
788.805 |
| SMC |
10 |
21.459 |
0.149 |
0.082 |
260.283 |
| SMC |
15 |
36.376 |
0.119 |
0.022 |
1666.872 |
| SMC |
30 |
67.819 |
0.116 |
0.011 |
6134.686 |
| Metro |
2 |
0.211 |
0.124 |
0.038 |
2.311 |
| Metro |
5 |
0.356 |
0.117 |
0.027 |
8.774 |
| Metro |
10 |
0.327 |
0.149 |
0.082 |
2.185 |
| Metro |
15 |
0.851 |
0.119 |
0.022 |
33.656 |
| Metro |
30 |
5.747 |
0.116 |
0.011 |
510.175 |
| DEMetro_Z |
2 |
0.271 |
0.124 |
0.038 |
3.885 |
| DEMetro_Z |
5 |
16.522 |
0.117 |
0.027 |
604.387 |
| DEMetro_Z |
10 |
6.976 |
0.149 |
0.082 |
83.393 |
| DEMetro_Z |
15 |
14.595 |
0.119 |
0.022 |
665.509 |
| DEMetro_Z |
30 |
47.293 |
0.116 |
0.011 |
4274.775 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.245 |
0.0349 |
1.685 |
| HMC |
5 |
5.207 |
1.87e-05 |
2.840 |
| HMC |
10 |
2.795 |
0.0115 |
13.563 |
| HMC |
15 |
4.538 |
0.000223 |
25.231 |
| HMC |
30 |
5.112 |
6.17e-05 |
42.944 |
| SMC |
2 |
14.564 |
5.9e-12 |
27.125 |
| SMC |
5 |
130.989 |
3.49e-30 |
257.773 |
| SMC |
10 |
142.223 |
4.85e-31 |
250.816 |
| SMC |
15 |
150.888 |
8.78e-32 |
234.845 |
| SMC |
30 |
163.890 |
3.5e-33 |
200.749 |
| Metro |
2 |
5.799 |
5.46e-06 |
3.719 |
| Metro |
5 |
9.057 |
2.21e-08 |
22.964 |
| Metro |
10 |
6.936 |
1.25e-06 |
24.401 |
| Metro |
15 |
7.200 |
7.59e-07 |
42.629 |
| Metro |
30 |
19.324 |
5.8e-14 |
172.664 |
| DEMetro_Z |
2 |
7.351 |
2.81e-07 |
6.804 |
| DEMetro_Z |
5 |
38.211 |
1.82e-19 |
248.132 |
| DEMetro_Z |
10 |
44.471 |
1.01e-20 |
251.536 |
| DEMetro_Z |
15 |
56.678 |
9.77e-23 |
268.316 |
| DEMetro_Z |
30 |
76.679 |
2.36e-25 |
235.293 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-10.254
|
3.51e-09
|
-2.293
|
| DEMetro_Z_vs_SMC |
1
|
-1.526
|
0.144
|
-0.341
|
| DEMetro_Z_vs_SMC |
2
|
0.118
|
0.907
|
0.026
|
| DEMetro_Z_vs_SMC |
3
|
6.720
|
2.01e-06
|
1.503
|
| DEMetro_Z_vs_SMC |
4
|
10.682
|
1.8e-09
|
2.389
|
| HMC_vs_Metro |
0
|
-2.015
|
0.0583
|
-0.451
|
| HMC_vs_Metro |
1
|
-7.748
|
2.69e-07
|
-1.732
|
| HMC_vs_Metro |
2
|
-2.812
|
0.0111
|
-0.629
|
| HMC_vs_Metro |
3
|
-2.308
|
0.0324
|
-0.516
|
| HMC_vs_Metro |
4
|
-11.483
|
5.43e-10
|
-2.568
|
| Metro_vs_DEMetro_Z |
0
|
-2.523
|
0.0207
|
-0.564
|
| Metro_vs_DEMetro_Z |
1
|
-32.486
|
4.1e-18
|
-7.264
|
| Metro_vs_DEMetro_Z |
2
|
-41.262
|
4.63e-20
|
-9.226
|
| Metro_vs_DEMetro_Z |
3
|
-27.074
|
1.22e-16
|
-6.054
|
| Metro_vs_DEMetro_Z |
4
|
-6.526
|
2.99e-06
|
-1.459
|
| HMC_vs_SMC |
0
|
-12.149
|
2.1e-10
|
-2.717
|
| HMC_vs_SMC |
1
|
-129.002
|
1.99e-29
|
-28.846
|
| HMC_vs_SMC |
2
|
-45.091
|
8.73e-21
|
-10.083
|
| HMC_vs_SMC |
3
|
-39.232
|
1.2e-19
|
-8.773
|
| HMC_vs_SMC |
4
|
-17.499
|
3.56e-13
|
-3.913
|
| Metro_vs_SMC |
0
|
-11.465
|
5.57e-10
|
-2.564
|
| Metro_vs_SMC |
1
|
-83.382
|
7.83e-26
|
-18.645
|
| Metro_vs_SMC |
2
|
-53.465
|
3.51e-22
|
-11.955
|
| Metro_vs_SMC |
3
|
-29.104
|
3.18e-17
|
-6.508
|
| Metro_vs_SMC |
4
|
-3.104
|
0.00584
|
-0.694
|
| HMC_vs_DEMetro_Z |
0
|
-4.807
|
0.000122
|
-1.075
|
| HMC_vs_DEMetro_Z |
1
|
-37.273
|
3.13e-19
|
-8.334
|
| HMC_vs_DEMetro_Z |
2
|
-37.072
|
3.46e-19
|
-8.290
|
| HMC_vs_DEMetro_Z |
3
|
-27.973
|
6.65e-17
|
-6.255
|
| HMC_vs_DEMetro_Z |
4
|
-20.999
|
1.31e-14
|
-4.696
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.022 |
0.014 |
0.005 |
1.685 |
| HMC |
5 |
0.020 |
0.015 |
0.002 |
2.840 |
| HMC |
10 |
0.039 |
0.015 |
0.002 |
13.563 |
| HMC |
15 |
0.061 |
0.016 |
0.002 |
25.231 |
| HMC |
30 |
0.101 |
0.015 |
0.002 |
42.944 |
| SMC |
2 |
0.141 |
0.014 |
0.005 |
27.125 |
| SMC |
5 |
0.505 |
0.015 |
0.002 |
257.773 |
| SMC |
10 |
0.456 |
0.015 |
0.002 |
250.816 |
| SMC |
15 |
0.436 |
0.016 |
0.002 |
234.845 |
| SMC |
30 |
0.414 |
0.015 |
0.002 |
200.749 |
| Metro |
2 |
0.032 |
0.014 |
0.005 |
3.719 |
| Metro |
5 |
0.058 |
0.015 |
0.002 |
22.964 |
| Metro |
10 |
0.058 |
0.015 |
0.002 |
24.401 |
| Metro |
15 |
0.092 |
0.016 |
0.002 |
42.629 |
| Metro |
30 |
0.359 |
0.015 |
0.002 |
172.664 |
| DEMetro_Z |
2 |
0.046 |
0.014 |
0.005 |
6.804 |
| DEMetro_Z |
5 |
0.487 |
0.015 |
0.002 |
248.132 |
| DEMetro_Z |
10 |
0.457 |
0.015 |
0.002 |
251.536 |
| DEMetro_Z |
15 |
0.495 |
0.016 |
0.002 |
268.316 |
| DEMetro_Z |
30 |
0.483 |
0.015 |
0.002 |
235.293 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.092 |
0.282 |
-0.332 |
| HMC |
5 |
0.876 |
0.387 |
0.300 |
| HMC |
10 |
-1.327 |
0.199 |
-0.302 |
| HMC |
15 |
1.413 |
0.174 |
4.591 |
| HMC |
30 |
1.180 |
0.253 |
8.451 |
| SMC |
2 |
1.450 |
0.156 |
0.558 |
| SMC |
5 |
4.819 |
0.000119 |
41.142 |
| SMC |
10 |
7.481 |
2.42e-07 |
7.596 |
| SMC |
15 |
18.443 |
1.25e-13 |
82.493 |
| SMC |
30 |
39.928 |
8.35e-20 |
426.800 |
| Metro |
2 |
3.120 |
0.00399 |
1.428 |
| Metro |
5 |
2.697 |
0.0123 |
1.595 |
| Metro |
10 |
0.810 |
0.424 |
0.209 |
| Metro |
15 |
3.524 |
0.00219 |
6.697 |
| Metro |
30 |
5.040 |
7.23e-05 |
38.312 |
| DEMetro_Z |
2 |
2.536 |
0.0161 |
1.029 |
| DEMetro_Z |
5 |
4.064 |
0.000661 |
68.636 |
| DEMetro_Z |
10 |
6.632 |
2.2e-06 |
15.530 |
| DEMetro_Z |
15 |
9.857 |
6.63e-09 |
304.163 |
| DEMetro_Z |
30 |
12.023 |
2.51e-10 |
1409.414 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.903
|
0.00912
|
-0.649
|
| HMC_vs_DEMetro_Z |
1
|
-4.026
|
0.000722
|
-0.900
|
| HMC_vs_DEMetro_Z |
2
|
-6.809
|
1.68e-06
|
-1.522
|
| HMC_vs_DEMetro_Z |
3
|
-9.490
|
1.21e-08
|
-2.122
|
| HMC_vs_DEMetro_Z |
4
|
-11.847
|
3.22e-10
|
-2.649
|
| Metro_vs_SMC |
0
|
1.711
|
0.103
|
0.383
|
| Metro_vs_SMC |
1
|
-4.618
|
0.000188
|
-1.033
|
| Metro_vs_SMC |
2
|
-7.194
|
7.82e-07
|
-1.609
|
| Metro_vs_SMC |
3
|
-14.800
|
6.97e-12
|
-3.309
|
| Metro_vs_SMC |
4
|
-31.586
|
6.93e-18
|
-7.063
|
| Metro_vs_DEMetro_Z |
0
|
0.788
|
0.44
|
0.176
|
| Metro_vs_DEMetro_Z |
1
|
-3.959
|
0.000841
|
-0.885
|
| Metro_vs_DEMetro_Z |
2
|
-6.652
|
2.31e-06
|
-1.487
|
| Metro_vs_DEMetro_Z |
3
|
-9.497
|
1.2e-08
|
-2.124
|
| Metro_vs_DEMetro_Z |
4
|
-11.951
|
2.78e-10
|
-2.672
|
| HMC_vs_Metro |
0
|
-3.846
|
0.00109
|
-0.860
|
| HMC_vs_Metro |
1
|
-1.967
|
0.064
|
-0.440
|
| HMC_vs_Metro |
2
|
-3.816
|
0.00117
|
-0.853
|
| HMC_vs_Metro |
3
|
-0.544
|
0.593
|
-0.122
|
| HMC_vs_Metro |
4
|
-2.899
|
0.00921
|
-0.648
|
| HMC_vs_SMC |
0
|
-2.563
|
0.019
|
-0.573
|
| HMC_vs_SMC |
1
|
-4.758
|
0.000137
|
-1.064
|
| HMC_vs_SMC |
2
|
-7.920
|
1.95e-07
|
-1.771
|
| HMC_vs_SMC |
3
|
-13.784
|
2.41e-11
|
-3.082
|
| HMC_vs_SMC |
4
|
-33.897
|
1.85e-18
|
-7.580
|
| DEMetro_Z_vs_SMC |
0
|
1.119
|
0.277
|
0.250
|
| DEMetro_Z_vs_SMC |
1
|
1.850
|
0.0799
|
0.414
|
| DEMetro_Z_vs_SMC |
2
|
3.007
|
0.00725
|
0.672
|
| DEMetro_Z_vs_SMC |
3
|
7.208
|
7.61e-07
|
1.612
|
| DEMetro_Z_vs_SMC |
4
|
8.442
|
7.47e-08
|
1.888
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.053 |
0.066 |
0.039 |
-0.332 |
| HMC |
5 |
0.076 |
0.067 |
0.029 |
0.300 |
| HMC |
10 |
0.068 |
0.095 |
0.090 |
-0.302 |
| HMC |
15 |
0.123 |
0.063 |
0.013 |
4.591 |
| HMC |
30 |
0.141 |
0.064 |
0.009 |
8.451 |
| SMC |
2 |
0.088 |
0.066 |
0.039 |
0.558 |
| SMC |
5 |
1.248 |
0.067 |
0.029 |
41.142 |
| SMC |
10 |
0.777 |
0.095 |
0.090 |
7.596 |
| SMC |
15 |
1.149 |
0.063 |
0.013 |
82.493 |
| SMC |
30 |
3.956 |
0.064 |
0.009 |
426.800 |
| Metro |
2 |
0.122 |
0.066 |
0.039 |
1.428 |
| Metro |
5 |
0.113 |
0.067 |
0.029 |
1.595 |
| Metro |
10 |
0.114 |
0.095 |
0.090 |
0.209 |
| Metro |
15 |
0.151 |
0.063 |
0.013 |
6.697 |
| Metro |
30 |
0.413 |
0.064 |
0.009 |
38.312 |
| DEMetro_Z |
2 |
0.107 |
0.066 |
0.039 |
1.029 |
| DEMetro_Z |
5 |
2.037 |
0.067 |
0.029 |
68.636 |
| DEMetro_Z |
10 |
1.488 |
0.095 |
0.090 |
15.530 |
| DEMetro_Z |
15 |
4.066 |
0.063 |
0.013 |
304.163 |
| DEMetro_Z |
30 |
12.916 |
0.064 |
0.009 |
1409.414 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.827 |
0.415 |
-0.217 |
| HMC |
5 |
-0.268 |
0.791 |
-0.065 |
| HMC |
10 |
-1.222 |
0.237 |
-0.273 |
| HMC |
15 |
1.012 |
0.324 |
1.389 |
| HMC |
30 |
1.036 |
0.312 |
1.042 |
| SMC |
2 |
-0.279 |
0.782 |
-0.071 |
| SMC |
5 |
11.645 |
3.87e-10 |
39.553 |
| SMC |
10 |
10.517 |
3.84e-11 |
2.615 |
| SMC |
15 |
61.511 |
1.68e-23 |
200.029 |
| SMC |
30 |
82.718 |
8.73e-26 |
867.705 |
| Metro |
2 |
-0.733 |
0.469 |
-0.197 |
| Metro |
5 |
-0.841 |
0.41 |
-0.190 |
| Metro |
10 |
-1.217 |
0.239 |
-0.272 |
| Metro |
15 |
1.196 |
0.243 |
0.709 |
| Metro |
30 |
2.461 |
0.0235 |
6.921 |
| DEMetro_Z |
2 |
-0.521 |
0.606 |
-0.138 |
| DEMetro_Z |
5 |
1.846 |
0.0805 |
19.264 |
| DEMetro_Z |
10 |
-0.296 |
0.77 |
-0.069 |
| DEMetro_Z |
15 |
5.026 |
7.44e-05 |
29.033 |
| DEMetro_Z |
30 |
6.807 |
1.69e-06 |
197.299 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-1.358
|
0.19
|
-0.304
|
| HMC_vs_SMC |
1
|
-11.665
|
4.17e-10
|
-2.608
|
| HMC_vs_SMC |
2
|
-26.295
|
2.09e-16
|
-5.880
|
| HMC_vs_SMC |
3
|
-60.495
|
3.4e-23
|
-13.527
|
| HMC_vs_SMC |
4
|
-81.622
|
1.17e-25
|
-18.251
|
| Metro_vs_DEMetro_Z |
0
|
-2.511
|
0.0213
|
-0.561
|
| Metro_vs_DEMetro_Z |
1
|
-1.867
|
0.0774
|
-0.418
|
| Metro_vs_DEMetro_Z |
2
|
-2.917
|
0.00884
|
-0.652
|
| Metro_vs_DEMetro_Z |
3
|
-4.837
|
0.000115
|
-1.082
|
| Metro_vs_DEMetro_Z |
4
|
-6.788
|
1.76e-06
|
-1.518
|
| HMC_vs_Metro |
0
|
-0.801
|
0.433
|
-0.179
|
| HMC_vs_Metro |
1
|
1.260
|
0.223
|
0.282
|
| HMC_vs_Metro |
2
|
-0.439
|
0.665
|
-0.098
|
| HMC_vs_Metro |
3
|
0.451
|
0.657
|
0.101
|
| HMC_vs_Metro |
4
|
-2.098
|
0.0495
|
-0.469
|
| HMC_vs_DEMetro_Z |
0
|
-4.523
|
0.000233
|
-1.011
|
| HMC_vs_DEMetro_Z |
1
|
-1.852
|
0.0796
|
-0.414
|
| HMC_vs_DEMetro_Z |
2
|
-2.879
|
0.00962
|
-0.644
|
| HMC_vs_DEMetro_Z |
3
|
-4.937
|
9.16e-05
|
-1.104
|
| HMC_vs_DEMetro_Z |
4
|
-6.770
|
1.82e-06
|
-1.514
|
| Metro_vs_SMC |
0
|
-1.167
|
0.258
|
-0.261
|
| Metro_vs_SMC |
1
|
-11.777
|
3.56e-10
|
-2.633
|
| Metro_vs_SMC |
2
|
-26.394
|
1.95e-16
|
-5.902
|
| Metro_vs_SMC |
3
|
-60.980
|
2.93e-23
|
-13.636
|
| Metro_vs_SMC |
4
|
-80.356
|
1.58e-25
|
-17.968
|
| DEMetro_Z_vs_SMC |
0
|
-0.647
|
0.525
|
-0.145
|
| DEMetro_Z_vs_SMC |
1
|
-1.918
|
0.0703
|
-0.429
|
| DEMetro_Z_vs_SMC |
2
|
-22.659
|
3.26e-15
|
-5.067
|
| DEMetro_Z_vs_SMC |
3
|
-27.471
|
9.3e-17
|
-6.143
|
| DEMetro_Z_vs_SMC |
4
|
-22.799
|
2.91e-15
|
-5.098
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
5.996 |
9.309 |
15.244 |
-0.217 |
| HMC |
5 |
8.328 |
9.700 |
21.181 |
-0.065 |
| HMC |
10 |
4.751 |
73.432 |
251.325 |
-0.273 |
| HMC |
15 |
21.468 |
7.127 |
10.327 |
1.389 |
| HMC |
30 |
15.655 |
6.949 |
8.351 |
1.042 |
| SMC |
2 |
8.223 |
9.309 |
15.244 |
-0.071 |
| SMC |
5 |
847.485 |
9.700 |
21.181 |
39.553 |
| SMC |
10 |
730.602 |
73.432 |
251.325 |
2.615 |
| SMC |
15 |
2072.829 |
7.127 |
10.327 |
200.029 |
| SMC |
30 |
7253.480 |
6.949 |
8.351 |
867.705 |
| Metro |
2 |
6.311 |
9.309 |
15.244 |
-0.197 |
| Metro |
5 |
5.667 |
9.700 |
21.181 |
-0.190 |
| Metro |
10 |
5.051 |
73.432 |
251.325 |
-0.272 |
| Metro |
15 |
14.448 |
7.127 |
10.327 |
0.709 |
| Metro |
30 |
64.747 |
6.949 |
8.351 |
6.921 |
| DEMetro_Z |
2 |
7.206 |
9.309 |
15.244 |
-0.138 |
| DEMetro_Z |
5 |
417.735 |
9.700 |
21.181 |
19.264 |
| DEMetro_Z |
10 |
56.011 |
73.432 |
251.325 |
-0.069 |
| DEMetro_Z |
15 |
306.951 |
7.127 |
10.327 |
29.033 |
| DEMetro_Z |
30 |
1654.669 |
6.949 |
8.351 |
197.299 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.794 |
0.433 |
0.222 |
| HMC |
5 |
3.921 |
0.000571 |
2.177 |
| HMC |
10 |
1.728 |
0.0926 |
0.487 |
| HMC |
15 |
1.195 |
0.247 |
26.379 |
| HMC |
30 |
2.513 |
0.0211 |
37.148 |
| SMC |
2 |
5.273 |
3.92e-05 |
9.368 |
| SMC |
5 |
20.586 |
1.88e-14 |
692.291 |
| SMC |
10 |
45.527 |
6.38e-21 |
237.719 |
| SMC |
15 |
111.999 |
2.83e-28 |
1582.750 |
| SMC |
30 |
159.974 |
3.34e-31 |
5947.322 |
| Metro |
2 |
5.519 |
5.63e-06 |
2.557 |
| Metro |
5 |
7.695 |
5.56e-08 |
4.826 |
| Metro |
10 |
3.919 |
0.000382 |
1.416 |
| Metro |
15 |
3.576 |
0.002 |
16.051 |
| Metro |
30 |
3.951 |
0.000856 |
169.227 |
| DEMetro_Z |
2 |
6.721 |
1.55e-07 |
2.906 |
| DEMetro_Z |
5 |
4.704 |
0.000155 |
162.816 |
| DEMetro_Z |
10 |
6.564 |
2.73e-06 |
39.654 |
| DEMetro_Z |
15 |
9.531 |
1.13e-08 |
511.201 |
| DEMetro_Z |
30 |
14.114 |
1.6e-11 |
2555.528 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.659
|
0.518
|
-0.147
|
| Metro_vs_DEMetro_Z |
1
|
-4.561
|
0.000214
|
-1.020
|
| Metro_vs_DEMetro_Z |
2
|
-6.344
|
4.36e-06
|
-1.419
|
| Metro_vs_DEMetro_Z |
3
|
-9.127
|
2.25e-08
|
-2.041
|
| Metro_vs_DEMetro_Z |
4
|
-14.051
|
1.73e-11
|
-3.142
|
| DEMetro_Z_vs_SMC |
0
|
-3.716
|
0.00147
|
-0.831
|
| DEMetro_Z_vs_SMC |
1
|
-10.639
|
1.92e-09
|
-2.379
|
| DEMetro_Z_vs_SMC |
2
|
-26.274
|
2.13e-16
|
-5.875
|
| DEMetro_Z_vs_SMC |
3
|
-19.780
|
3.89e-14
|
-4.423
|
| DEMetro_Z_vs_SMC |
4
|
-19.060
|
7.63e-14
|
-4.262
|
| HMC_vs_DEMetro_Z |
0
|
-8.130
|
1.32e-07
|
-1.818
|
| HMC_vs_DEMetro_Z |
1
|
-4.615
|
0.000189
|
-1.032
|
| HMC_vs_DEMetro_Z |
2
|
-6.532
|
2.95e-06
|
-1.461
|
| HMC_vs_DEMetro_Z |
3
|
-9.148
|
2.17e-08
|
-2.045
|
| HMC_vs_DEMetro_Z |
4
|
-13.674
|
2.77e-11
|
-3.057
|
| HMC_vs_Metro |
0
|
-6.078
|
7.62e-06
|
-1.359
|
| HMC_vs_Metro |
1
|
-3.703
|
0.00151
|
-0.828
|
| HMC_vs_Metro |
2
|
-2.675
|
0.015
|
-0.598
|
| HMC_vs_Metro |
3
|
0.447
|
0.66
|
0.100
|
| HMC_vs_Metro |
4
|
-2.758
|
0.0125
|
-0.617
|
| HMC_vs_SMC |
0
|
-5.255
|
4.51e-05
|
-1.175
|
| HMC_vs_SMC |
1
|
-20.530
|
1.98e-14
|
-4.591
|
| HMC_vs_SMC |
2
|
-45.475
|
7.44e-21
|
-10.169
|
| HMC_vs_SMC |
3
|
-63.895
|
1.21e-23
|
-14.287
|
| HMC_vs_SMC |
4
|
-131.058
|
1.48e-29
|
-29.306
|
| Metro_vs_SMC |
0
|
-3.742
|
0.00138
|
-0.837
|
| Metro_vs_SMC |
1
|
-20.620
|
1.83e-14
|
-4.611
|
| Metro_vs_SMC |
2
|
-44.944
|
9.28e-21
|
-10.050
|
| Metro_vs_SMC |
3
|
-108.838
|
5.01e-28
|
-24.337
|
| Metro_vs_SMC |
4
|
-111.895
|
2.96e-28
|
-25.021
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.133 |
0.124 |
0.038 |
0.222 |
| HMC |
5 |
0.177 |
0.117 |
0.027 |
2.177 |
| HMC |
10 |
0.188 |
0.149 |
0.082 |
0.487 |
| HMC |
15 |
0.693 |
0.119 |
0.022 |
26.379 |
| HMC |
30 |
0.526 |
0.116 |
0.011 |
37.148 |
| SMC |
2 |
0.477 |
0.124 |
0.038 |
9.368 |
| SMC |
5 |
18.908 |
0.117 |
0.027 |
692.291 |
| SMC |
10 |
19.612 |
0.149 |
0.082 |
237.719 |
| SMC |
15 |
34.546 |
0.119 |
0.022 |
1582.750 |
| SMC |
30 |
65.751 |
0.116 |
0.011 |
5947.322 |
| Metro |
2 |
0.221 |
0.124 |
0.038 |
2.557 |
| Metro |
5 |
0.248 |
0.117 |
0.027 |
4.826 |
| Metro |
10 |
0.264 |
0.149 |
0.082 |
1.416 |
| Metro |
15 |
0.468 |
0.119 |
0.022 |
16.051 |
| Metro |
30 |
1.984 |
0.116 |
0.011 |
169.227 |
| DEMetro_Z |
2 |
0.234 |
0.124 |
0.038 |
2.906 |
| DEMetro_Z |
5 |
4.537 |
0.117 |
0.027 |
162.816 |
| DEMetro_Z |
10 |
3.395 |
0.149 |
0.082 |
39.654 |
| DEMetro_Z |
15 |
11.239 |
0.119 |
0.022 |
511.201 |
| DEMetro_Z |
30 |
28.319 |
0.116 |
0.011 |
2555.528 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.637 |
0.11 |
0.461 |
| HMC |
5 |
5.239 |
2.32e-05 |
3.463 |
| HMC |
10 |
5.924 |
8.62e-06 |
8.395 |
| HMC |
15 |
1.854 |
0.0794 |
24.950 |
| HMC |
30 |
2.278 |
0.0344 |
41.016 |
| SMC |
2 |
7.227 |
6.62e-07 |
17.524 |
| SMC |
5 |
61.581 |
1.94e-23 |
264.590 |
| SMC |
10 |
123.994 |
1.13e-29 |
253.604 |
| SMC |
15 |
125.749 |
6.82e-30 |
237.483 |
| SMC |
30 |
157.186 |
1.18e-32 |
201.604 |
| Metro |
2 |
6.130 |
3.07e-06 |
4.503 |
| Metro |
5 |
9.729 |
5.7e-09 |
15.804 |
| Metro |
10 |
6.193 |
5.72e-06 |
19.535 |
| Metro |
15 |
5.786 |
1.4e-05 |
36.866 |
| Metro |
30 |
7.514 |
4.18e-07 |
103.664 |
| DEMetro_Z |
2 |
7.463 |
7.08e-08 |
4.291 |
| DEMetro_Z |
5 |
10.848 |
1.39e-09 |
150.467 |
| DEMetro_Z |
10 |
16.206 |
1.39e-12 |
229.434 |
| DEMetro_Z |
15 |
30.112 |
1.64e-17 |
283.035 |
| DEMetro_Z |
30 |
39.573 |
9.44e-20 |
265.721 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-5.114
|
6.16e-05
|
-1.144
|
| DEMetro_Z_vs_SMC |
1
|
-9.156
|
2.14e-08
|
-2.047
|
| DEMetro_Z_vs_SMC |
2
|
-1.637
|
0.118
|
-0.366
|
| DEMetro_Z_vs_SMC |
3
|
5.277
|
4.3e-05
|
1.180
|
| DEMetro_Z_vs_SMC |
4
|
9.064
|
2.5e-08
|
2.027
|
| HMC_vs_Metro |
0
|
-5.717
|
1.65e-05
|
-1.278
|
| HMC_vs_Metro |
1
|
-7.287
|
6.51e-07
|
-1.630
|
| HMC_vs_Metro |
2
|
-2.985
|
0.00761
|
-0.667
|
| HMC_vs_Metro |
3
|
-0.767
|
0.453
|
-0.171
|
| HMC_vs_Metro |
4
|
-2.877
|
0.00966
|
-0.643
|
| Metro_vs_DEMetro_Z |
0
|
0.216
|
0.831
|
0.048
|
| Metro_vs_DEMetro_Z |
1
|
-9.289
|
1.7e-08
|
-2.077
|
| Metro_vs_DEMetro_Z |
2
|
-13.898
|
2.09e-11
|
-3.108
|
| Metro_vs_DEMetro_Z |
3
|
-21.478
|
8.68e-15
|
-4.803
|
| Metro_vs_DEMetro_Z |
4
|
-11.287
|
7.24e-10
|
-2.524
|
| HMC_vs_SMC |
0
|
-6.926
|
1.33e-06
|
-1.549
|
| HMC_vs_SMC |
1
|
-58.440
|
6.54e-23
|
-13.067
|
| HMC_vs_SMC |
2
|
-106.544
|
7.51e-28
|
-23.824
|
| HMC_vs_SMC |
3
|
-15.027
|
5.33e-12
|
-3.360
|
| HMC_vs_SMC |
4
|
-9.012
|
2.73e-08
|
-2.015
|
| Metro_vs_SMC |
0
|
-4.968
|
8.55e-05
|
-1.111
|
| Metro_vs_SMC |
1
|
-50.063
|
1.21e-21
|
-11.194
|
| Metro_vs_SMC |
2
|
-57.062
|
1.03e-22
|
-12.759
|
| Metro_vs_SMC |
3
|
-31.660
|
6.63e-18
|
-7.079
|
| Metro_vs_SMC |
4
|
-7.198
|
7.75e-07
|
-1.610
|
| HMC_vs_DEMetro_Z |
0
|
-7.315
|
6.17e-07
|
-1.636
|
| HMC_vs_DEMetro_Z |
1
|
-10.424
|
2.68e-09
|
-2.331
|
| HMC_vs_DEMetro_Z |
2
|
-15.441
|
3.3e-12
|
-3.453
|
| HMC_vs_DEMetro_Z |
3
|
-13.985
|
1.87e-11
|
-3.127
|
| HMC_vs_DEMetro_Z |
4
|
-11.763
|
3.62e-10
|
-2.630
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.017 |
0.014 |
0.005 |
0.461 |
| HMC |
5 |
0.021 |
0.015 |
0.002 |
3.463 |
| HMC |
10 |
0.030 |
0.015 |
0.002 |
8.395 |
| HMC |
15 |
0.060 |
0.016 |
0.002 |
24.950 |
| HMC |
30 |
0.097 |
0.015 |
0.002 |
41.016 |
| SMC |
2 |
0.096 |
0.014 |
0.005 |
17.524 |
| SMC |
5 |
0.518 |
0.015 |
0.002 |
264.590 |
| SMC |
10 |
0.461 |
0.015 |
0.002 |
253.604 |
| SMC |
15 |
0.440 |
0.016 |
0.002 |
237.483 |
| SMC |
30 |
0.416 |
0.015 |
0.002 |
201.604 |
| Metro |
2 |
0.035 |
0.014 |
0.005 |
4.503 |
| Metro |
5 |
0.045 |
0.015 |
0.002 |
15.804 |
| Metro |
10 |
0.049 |
0.015 |
0.002 |
19.535 |
| Metro |
15 |
0.082 |
0.016 |
0.002 |
36.866 |
| Metro |
30 |
0.221 |
0.015 |
0.002 |
103.664 |
| DEMetro_Z |
2 |
0.034 |
0.014 |
0.005 |
4.291 |
| DEMetro_Z |
5 |
0.301 |
0.015 |
0.002 |
150.467 |
| DEMetro_Z |
10 |
0.419 |
0.015 |
0.002 |
229.434 |
| DEMetro_Z |
15 |
0.522 |
0.016 |
0.002 |
283.035 |
| DEMetro_Z |
30 |
0.544 |
0.015 |
0.002 |
265.721 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_Multimodality
(Mixture,
dimension,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
6.644 |
2.27e-06 |
25.405 |
| HMC |
5 |
3.216 |
0.00453 |
14.954 |
| HMC |
10 |
3.785 |
0.00125 |
25.600 |
| HMC |
15 |
3.503 |
0.00237 |
39.641 |
| HMC |
30 |
5.477 |
2.76e-05 |
64.979 |
| SMC |
2 |
0.458 |
0.649 |
0.158 |
| SMC |
5 |
-0.167 |
0.868 |
-0.049 |
| SMC |
10 |
-0.744 |
0.462 |
-0.200 |
| SMC |
15 |
1.180 |
0.248 |
0.627 |
| SMC |
30 |
0.985 |
0.334 |
0.570 |
| Metro |
2 |
5.906 |
1.08e-05 |
28.676 |
| Metro |
5 |
6.204 |
5.7e-06 |
26.861 |
| Metro |
10 |
4.850 |
0.00011 |
28.334 |
| Metro |
15 |
4.875 |
0.000105 |
48.921 |
| Metro |
30 |
5.265 |
4.4e-05 |
55.595 |
| DEMetro_Z |
2 |
5.637 |
1.92e-05 |
23.279 |
| DEMetro_Z |
5 |
9.584 |
1.02e-08 |
71.532 |
| DEMetro_Z |
10 |
15.352 |
3.63e-12 |
228.424 |
| DEMetro_Z |
15 |
22.303 |
4.33e-15 |
488.284 |
| DEMetro_Z |
30 |
39.511 |
1.04e-19 |
974.763 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
0.330
|
0.745
|
0.074
|
| HMC_vs_DEMetro_Z |
1
|
-6.606
|
2.54e-06
|
-1.477
|
| HMC_vs_DEMetro_Z |
2
|
-12.195
|
1.97e-10
|
-2.727
|
| HMC_vs_DEMetro_Z |
3
|
-19.454
|
5.26e-14
|
-4.350
|
| HMC_vs_DEMetro_Z |
4
|
-34.712
|
1.19e-18
|
-7.762
|
| Metro_vs_SMC |
0
|
5.882
|
1.15e-05
|
1.315
|
| Metro_vs_SMC |
1
|
6.185
|
6.07e-06
|
1.383
|
| Metro_vs_SMC |
2
|
4.864
|
0.000108
|
1.088
|
| Metro_vs_SMC |
3
|
4.761
|
0.000136
|
1.065
|
| Metro_vs_SMC |
4
|
5.289
|
4.18e-05
|
1.183
|
| Metro_vs_DEMetro_Z |
0
|
0.823
|
0.421
|
0.184
|
| Metro_vs_DEMetro_Z |
1
|
-5.615
|
2.05e-05
|
-1.256
|
| Metro_vs_DEMetro_Z |
2
|
-12.356
|
1.58e-10
|
-2.763
|
| Metro_vs_DEMetro_Z |
3
|
-24.410
|
8.28e-16
|
-5.458
|
| Metro_vs_DEMetro_Z |
4
|
-33.312
|
2.56e-18
|
-7.449
|
| HMC_vs_Metro |
0
|
-0.990
|
0.334
|
-0.221
|
| HMC_vs_Metro |
1
|
-2.635
|
0.0163
|
-0.589
|
| HMC_vs_Metro |
2
|
-0.478
|
0.638
|
-0.107
|
| HMC_vs_Metro |
3
|
-0.587
|
0.564
|
-0.131
|
| HMC_vs_Metro |
4
|
1.368
|
0.187
|
0.306
|
| HMC_vs_SMC |
0
|
6.516
|
3.06e-06
|
1.457
|
| HMC_vs_SMC |
1
|
3.243
|
0.00429
|
0.725
|
| HMC_vs_SMC |
2
|
3.828
|
0.00113
|
0.856
|
| HMC_vs_SMC |
3
|
3.477
|
0.00252
|
0.778
|
| HMC_vs_SMC |
4
|
5.426
|
3.1e-05
|
1.213
|
| DEMetro_Z_vs_SMC |
0
|
5.592
|
2.16e-05
|
1.250
|
| DEMetro_Z_vs_SMC |
1
|
9.498
|
1.2e-08
|
2.124
|
| DEMetro_Z_vs_SMC |
2
|
15.359
|
3.63e-12
|
3.434
|
| DEMetro_Z_vs_SMC |
3
|
22.306
|
4.34e-15
|
4.988
|
| DEMetro_Z_vs_SMC |
4
|
39.250
|
1.19e-19
|
8.777
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.683 |
0.090 |
0.063 |
25.405 |
| HMC |
5 |
0.623 |
0.053 |
0.038 |
14.954 |
| HMC |
10 |
0.674 |
0.044 |
0.025 |
25.600 |
| HMC |
15 |
0.526 |
0.036 |
0.012 |
39.641 |
| HMC |
30 |
0.505 |
0.032 |
0.007 |
64.979 |
| SMC |
2 |
0.100 |
0.090 |
0.063 |
0.158 |
| SMC |
5 |
0.051 |
0.053 |
0.038 |
-0.049 |
| SMC |
10 |
0.039 |
0.044 |
0.025 |
-0.200 |
| SMC |
15 |
0.044 |
0.036 |
0.012 |
0.627 |
| SMC |
30 |
0.036 |
0.032 |
0.007 |
0.570 |
| Metro |
2 |
1.889 |
0.090 |
0.063 |
28.676 |
| Metro |
5 |
1.076 |
0.053 |
0.038 |
26.861 |
| Metro |
10 |
0.741 |
0.044 |
0.025 |
28.334 |
| Metro |
15 |
0.640 |
0.036 |
0.012 |
48.921 |
| Metro |
30 |
0.437 |
0.032 |
0.007 |
55.595 |
| DEMetro_Z |
2 |
1.550 |
0.090 |
0.063 |
23.279 |
| DEMetro_Z |
5 |
2.778 |
0.053 |
0.038 |
71.532 |
| DEMetro_Z |
10 |
5.664 |
0.044 |
0.025 |
228.424 |
| DEMetro_Z |
15 |
6.064 |
0.036 |
0.012 |
488.284 |
| DEMetro_Z |
30 |
7.127 |
0.032 |
0.007 |
974.763 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
4.649 |
0.000174 |
48.701 |
| HMC |
5 |
2.594 |
0.0178 |
30.101 |
| HMC |
10 |
3.134 |
0.00547 |
97.239 |
| HMC |
15 |
2.989 |
0.00754 |
69.221 |
| HMC |
30 |
3.935 |
0.00089 |
100.923 |
| SMC |
2 |
1.069 |
0.292 |
0.356 |
| SMC |
5 |
0.938 |
0.355 |
0.262 |
| SMC |
10 |
0.669 |
0.508 |
0.281 |
| SMC |
15 |
0.573 |
0.57 |
0.173 |
| SMC |
30 |
1.101 |
0.28 |
0.531 |
| Metro |
2 |
4.160 |
0.000532 |
66.116 |
| Metro |
5 |
3.834 |
0.00112 |
51.672 |
| Metro |
10 |
3.510 |
0.00234 |
95.001 |
| Metro |
15 |
3.519 |
0.00229 |
78.107 |
| Metro |
30 |
3.648 |
0.00171 |
77.196 |
| DEMetro_Z |
2 |
3.307 |
0.00371 |
42.920 |
| DEMetro_Z |
5 |
9.182 |
2.04e-08 |
478.093 |
| DEMetro_Z |
10 |
17.276 |
4.48e-13 |
3429.162 |
| DEMetro_Z |
15 |
17.271 |
4.5e-13 |
4097.380 |
| DEMetro_Z |
30 |
29.267 |
2.87e-17 |
7549.873 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
4.595
|
0.000198
|
1.027
|
| HMC_vs_SMC |
1
|
2.564
|
0.019
|
0.573
|
| HMC_vs_SMC |
2
|
3.113
|
0.00573
|
0.696
|
| HMC_vs_SMC |
3
|
2.973
|
0.00782
|
0.665
|
| HMC_vs_SMC |
4
|
3.938
|
0.000883
|
0.881
|
| Metro_vs_DEMetro_Z |
0
|
1.078
|
0.294
|
0.241
|
| Metro_vs_DEMetro_Z |
1
|
-7.659
|
3.18e-07
|
-1.713
|
| Metro_vs_DEMetro_Z |
2
|
-16.166
|
1.46e-12
|
-3.615
|
| Metro_vs_DEMetro_Z |
3
|
-17.333
|
4.22e-13
|
-3.876
|
| Metro_vs_DEMetro_Z |
4
|
-29.147
|
3.1e-17
|
-6.518
|
| HMC_vs_Metro |
0
|
-1.430
|
0.169
|
-0.320
|
| HMC_vs_Metro |
1
|
-1.913
|
0.071
|
-0.428
|
| HMC_vs_Metro |
2
|
0.083
|
0.935
|
0.019
|
| HMC_vs_Metro |
3
|
-0.252
|
0.803
|
-0.056
|
| HMC_vs_Metro |
4
|
1.673
|
0.111
|
0.374
|
| HMC_vs_DEMetro_Z |
0
|
0.304
|
0.765
|
0.068
|
| HMC_vs_DEMetro_Z |
1
|
-7.950
|
1.84e-07
|
-1.778
|
| HMC_vs_DEMetro_Z |
2
|
-15.506
|
3.07e-12
|
-3.467
|
| HMC_vs_DEMetro_Z |
3
|
-17.075
|
5.52e-13
|
-3.818
|
| HMC_vs_DEMetro_Z |
4
|
-29.446
|
2.56e-17
|
-6.584
|
| Metro_vs_SMC |
0
|
4.139
|
0.000558
|
0.926
|
| Metro_vs_SMC |
1
|
3.806
|
0.00119
|
0.851
|
| Metro_vs_SMC |
2
|
3.483
|
0.00249
|
0.779
|
| Metro_vs_SMC |
3
|
3.505
|
0.00237
|
0.784
|
| Metro_vs_SMC |
4
|
3.639
|
0.00175
|
0.814
|
| DEMetro_Z_vs_SMC |
0
|
3.279
|
0.00395
|
0.733
|
| DEMetro_Z_vs_SMC |
1
|
9.190
|
2.01e-08
|
2.055
|
| DEMetro_Z_vs_SMC |
2
|
17.266
|
4.53e-13
|
3.861
|
| DEMetro_Z_vs_SMC |
3
|
17.268
|
4.52e-13
|
3.861
|
| DEMetro_Z_vs_SMC |
4
|
29.280
|
2.84e-17
|
6.547
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
5.741 |
0.121 |
0.115 |
48.701 |
| HMC |
5 |
2.269 |
0.091 |
0.072 |
30.101 |
| HMC |
10 |
3.144 |
0.070 |
0.032 |
97.239 |
| HMC |
15 |
2.490 |
0.067 |
0.035 |
69.221 |
| HMC |
30 |
2.159 |
0.056 |
0.021 |
100.923 |
| SMC |
2 |
0.162 |
0.121 |
0.115 |
0.356 |
| SMC |
5 |
0.110 |
0.091 |
0.072 |
0.262 |
| SMC |
10 |
0.079 |
0.070 |
0.032 |
0.281 |
| SMC |
15 |
0.074 |
0.067 |
0.035 |
0.173 |
| SMC |
30 |
0.067 |
0.056 |
0.021 |
0.531 |
| Metro |
2 |
7.751 |
0.121 |
0.115 |
66.116 |
| Metro |
5 |
3.830 |
0.091 |
0.072 |
51.672 |
| Metro |
10 |
3.073 |
0.070 |
0.032 |
95.001 |
| Metro |
15 |
2.801 |
0.067 |
0.035 |
78.107 |
| Metro |
30 |
1.665 |
0.056 |
0.021 |
77.196 |
| DEMetro_Z |
2 |
5.074 |
0.121 |
0.115 |
42.920 |
| DEMetro_Z |
5 |
34.689 |
0.091 |
0.072 |
478.093 |
| DEMetro_Z |
10 |
108.491 |
0.070 |
0.032 |
3429.162 |
| DEMetro_Z |
15 |
143.442 |
0.067 |
0.035 |
4097.380 |
| DEMetro_Z |
30 |
157.410 |
0.056 |
0.021 |
7549.873 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
6.812 |
1.61e-06 |
26.403 |
| HMC |
5 |
3.278 |
0.00394 |
15.389 |
| HMC |
10 |
3.710 |
0.00148 |
29.181 |
| HMC |
15 |
3.532 |
0.00223 |
49.376 |
| HMC |
30 |
5.377 |
3.44e-05 |
83.768 |
| SMC |
2 |
0.162 |
0.872 |
0.055 |
| SMC |
5 |
-0.197 |
0.845 |
-0.056 |
| SMC |
10 |
-0.655 |
0.517 |
-0.172 |
| SMC |
15 |
1.306 |
0.203 |
0.738 |
| SMC |
30 |
1.321 |
0.199 |
0.815 |
| Metro |
2 |
5.844 |
1.23e-05 |
30.230 |
| Metro |
5 |
5.987 |
9.04e-06 |
27.159 |
| Metro |
10 |
4.878 |
0.000104 |
31.904 |
| Metro |
15 |
4.805 |
0.000123 |
60.840 |
| Metro |
30 |
5.213 |
4.95e-05 |
71.305 |
| DEMetro_Z |
2 |
5.620 |
1.99e-05 |
25.073 |
| DEMetro_Z |
5 |
12.645 |
1.05e-10 |
111.775 |
| DEMetro_Z |
10 |
29.281 |
2.81e-17 |
444.902 |
| DEMetro_Z |
15 |
30.090 |
1.71e-17 |
1122.650 |
| DEMetro_Z |
30 |
71.902 |
1.29e-24 |
2174.952 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.736
|
0.471
|
0.165
|
| Metro_vs_DEMetro_Z |
1
|
-8.737
|
4.42e-08
|
-1.954
|
| Metro_vs_DEMetro_Z |
2
|
-24.794
|
6.21e-16
|
-5.544
|
| Metro_vs_DEMetro_Z |
3
|
-31.855
|
5.91e-18
|
-7.123
|
| Metro_vs_DEMetro_Z |
4
|
-63.566
|
1.33e-23
|
-14.214
|
| DEMetro_Z_vs_SMC |
0
|
5.592
|
2.16e-05
|
1.250
|
| DEMetro_Z_vs_SMC |
1
|
12.531
|
1.24e-10
|
2.802
|
| DEMetro_Z_vs_SMC |
2
|
29.354
|
2.71e-17
|
6.564
|
| DEMetro_Z_vs_SMC |
3
|
30.049
|
1.76e-17
|
6.719
|
| DEMetro_Z_vs_SMC |
4
|
71.489
|
1.45e-24
|
15.985
|
| HMC_vs_DEMetro_Z |
0
|
0.197
|
0.846
|
0.044
|
| HMC_vs_DEMetro_Z |
1
|
-9.419
|
1.37e-08
|
-2.106
|
| HMC_vs_DEMetro_Z |
2
|
-21.803
|
6.59e-15
|
-4.875
|
| HMC_vs_DEMetro_Z |
3
|
-28.324
|
5.27e-17
|
-6.333
|
| HMC_vs_DEMetro_Z |
4
|
-68.088
|
3.64e-24
|
-15.225
|
| HMC_vs_Metro |
0
|
-1.081
|
0.293
|
-0.242
|
| HMC_vs_Metro |
1
|
-2.442
|
0.0246
|
-0.546
|
| HMC_vs_Metro |
2
|
-0.393
|
0.698
|
-0.088
|
| HMC_vs_Metro |
3
|
-0.584
|
0.566
|
-0.131
|
| HMC_vs_Metro |
4
|
1.303
|
0.208
|
0.291
|
| HMC_vs_SMC |
0
|
6.756
|
1.87e-06
|
1.511
|
| HMC_vs_SMC |
1
|
3.293
|
0.00382
|
0.736
|
| HMC_vs_SMC |
2
|
3.737
|
0.0014
|
0.836
|
| HMC_vs_SMC |
3
|
3.508
|
0.00235
|
0.785
|
| HMC_vs_SMC |
4
|
5.323
|
3.88e-05
|
1.190
|
| Metro_vs_SMC |
0
|
5.859
|
1.21e-05
|
1.310
|
| Metro_vs_SMC |
1
|
5.977
|
9.42e-06
|
1.337
|
| Metro_vs_SMC |
2
|
4.884
|
0.000103
|
1.092
|
| Metro_vs_SMC |
3
|
4.701
|
0.000155
|
1.051
|
| Metro_vs_SMC |
4
|
5.224
|
4.83e-05
|
1.168
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.504 |
0.099 |
0.053 |
26.403 |
| HMC |
5 |
0.536 |
0.061 |
0.031 |
15.389 |
| HMC |
10 |
0.557 |
0.050 |
0.017 |
29.181 |
| HMC |
15 |
0.430 |
0.044 |
0.008 |
49.376 |
| HMC |
30 |
0.416 |
0.039 |
0.004 |
83.768 |
| SMC |
2 |
0.102 |
0.099 |
0.053 |
0.055 |
| SMC |
5 |
0.059 |
0.061 |
0.031 |
-0.056 |
| SMC |
10 |
0.047 |
0.050 |
0.017 |
-0.172 |
| SMC |
15 |
0.050 |
0.044 |
0.008 |
0.738 |
| SMC |
30 |
0.043 |
0.039 |
0.004 |
0.815 |
| Metro |
2 |
1.708 |
0.099 |
0.053 |
30.230 |
| Metro |
5 |
0.900 |
0.061 |
0.031 |
27.159 |
| Metro |
10 |
0.604 |
0.050 |
0.017 |
31.904 |
| Metro |
15 |
0.519 |
0.044 |
0.008 |
60.840 |
| Metro |
30 |
0.360 |
0.039 |
0.004 |
71.305 |
| DEMetro_Z |
2 |
1.434 |
0.099 |
0.053 |
25.073 |
| DEMetro_Z |
5 |
3.512 |
0.061 |
0.031 |
111.775 |
| DEMetro_Z |
10 |
7.775 |
0.050 |
0.017 |
444.902 |
| DEMetro_Z |
15 |
8.811 |
0.044 |
0.008 |
1122.650 |
| DEMetro_Z |
30 |
9.823 |
0.039 |
0.004 |
2174.952 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
6.859 |
1.48e-06 |
31.431 |
| HMC |
5 |
3.247 |
0.00423 |
16.635 |
| HMC |
10 |
3.822 |
0.00115 |
28.954 |
| HMC |
15 |
3.521 |
0.00228 |
47.252 |
| HMC |
30 |
5.370 |
3.49e-05 |
75.768 |
| SMC |
2 |
0.627 |
0.534 |
0.228 |
| SMC |
5 |
-0.458 |
0.65 |
-0.128 |
| SMC |
10 |
-0.586 |
0.562 |
-0.155 |
| SMC |
15 |
1.150 |
0.261 |
0.667 |
| SMC |
30 |
1.168 |
0.254 |
0.666 |
| Metro |
2 |
6.136 |
6.64e-06 |
35.125 |
| Metro |
5 |
6.261 |
5.08e-06 |
29.829 |
| Metro |
10 |
4.865 |
0.000107 |
32.368 |
| Metro |
15 |
4.836 |
0.000115 |
58.879 |
| Metro |
30 |
5.236 |
4.69e-05 |
64.666 |
| DEMetro_Z |
2 |
5.829 |
1.27e-05 |
28.812 |
| DEMetro_Z |
5 |
17.526 |
2.82e-13 |
52.519 |
| DEMetro_Z |
10 |
52.181 |
1.47e-22 |
89.151 |
| DEMetro_Z |
15 |
48.400 |
1.63e-21 |
158.357 |
| DEMetro_Z |
30 |
54.095 |
2.25e-22 |
224.943 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.775
|
1.45e-05
|
1.291
|
| DEMetro_Z_vs_SMC |
1
|
17.222
|
4.74e-13
|
3.851
|
| DEMetro_Z_vs_SMC |
2
|
52.056
|
5.82e-22
|
11.640
|
| DEMetro_Z_vs_SMC |
3
|
48.122
|
2.56e-21
|
10.760
|
| DEMetro_Z_vs_SMC |
4
|
55.605
|
1.67e-22
|
12.434
|
| HMC_vs_Metro |
0
|
-0.978
|
0.341
|
-0.219
|
| HMC_vs_Metro |
1
|
-2.686
|
0.0146
|
-0.601
|
| HMC_vs_Metro |
2
|
-0.517
|
0.611
|
-0.116
|
| HMC_vs_Metro |
3
|
-0.608
|
0.55
|
-0.136
|
| HMC_vs_Metro |
4
|
1.334
|
0.198
|
0.298
|
| Metro_vs_DEMetro_Z |
0
|
0.815
|
0.425
|
0.182
|
| Metro_vs_DEMetro_Z |
1
|
-4.460
|
0.000269
|
-0.997
|
| Metro_vs_DEMetro_Z |
2
|
-8.205
|
1.15e-07
|
-1.835
|
| Metro_vs_DEMetro_Z |
3
|
-8.780
|
4.1e-08
|
-1.963
|
| Metro_vs_DEMetro_Z |
4
|
-12.484
|
1.32e-10
|
-2.792
|
| HMC_vs_SMC |
0
|
6.735
|
1.95e-06
|
1.506
|
| HMC_vs_SMC |
1
|
3.276
|
0.00397
|
0.733
|
| HMC_vs_SMC |
2
|
3.848
|
0.00108
|
0.861
|
| HMC_vs_SMC |
3
|
3.501
|
0.00239
|
0.783
|
| HMC_vs_SMC |
4
|
5.317
|
3.94e-05
|
1.189
|
| Metro_vs_SMC |
0
|
6.117
|
7.01e-06
|
1.368
|
| Metro_vs_SMC |
1
|
6.269
|
5.1e-06
|
1.402
|
| Metro_vs_SMC |
2
|
4.864
|
0.000108
|
1.088
|
| Metro_vs_SMC |
3
|
4.725
|
0.000147
|
1.057
|
| Metro_vs_SMC |
4
|
5.248
|
4.58e-05
|
1.174
|
| HMC_vs_DEMetro_Z |
0
|
0.343
|
0.736
|
0.077
|
| HMC_vs_DEMetro_Z |
1
|
-6.092
|
7.4e-06
|
-1.362
|
| HMC_vs_DEMetro_Z |
2
|
-7.541
|
3.98e-07
|
-1.686
|
| HMC_vs_DEMetro_Z |
3
|
-7.931
|
1.91e-07
|
-1.773
|
| HMC_vs_DEMetro_Z |
4
|
-9.633
|
9.58e-09
|
-2.154
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.255 |
0.013 |
0.008 |
31.431 |
| HMC |
5 |
0.143 |
0.012 |
0.008 |
16.635 |
| HMC |
10 |
0.201 |
0.014 |
0.006 |
28.954 |
| HMC |
15 |
0.179 |
0.013 |
0.004 |
47.252 |
| HMC |
30 |
0.206 |
0.014 |
0.003 |
75.768 |
| SMC |
2 |
0.015 |
0.013 |
0.008 |
0.228 |
| SMC |
5 |
0.011 |
0.012 |
0.008 |
-0.128 |
| SMC |
10 |
0.013 |
0.014 |
0.006 |
-0.155 |
| SMC |
15 |
0.016 |
0.013 |
0.004 |
0.667 |
| SMC |
30 |
0.016 |
0.014 |
0.003 |
0.666 |
| Metro |
2 |
0.284 |
0.013 |
0.008 |
35.125 |
| Metro |
5 |
0.247 |
0.012 |
0.008 |
29.829 |
| Metro |
10 |
0.223 |
0.014 |
0.006 |
32.368 |
| Metro |
15 |
0.220 |
0.013 |
0.004 |
58.879 |
| Metro |
30 |
0.178 |
0.014 |
0.003 |
64.666 |
| DEMetro_Z |
2 |
0.235 |
0.013 |
0.008 |
28.812 |
| DEMetro_Z |
5 |
0.425 |
0.012 |
0.008 |
52.519 |
| DEMetro_Z |
10 |
0.590 |
0.014 |
0.006 |
89.151 |
| DEMetro_Z |
15 |
0.569 |
0.013 |
0.004 |
158.357 |
| DEMetro_Z |
30 |
0.582 |
0.014 |
0.003 |
224.943 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
197.060 |
3.02e-58 |
65.947 |
| HMC |
5 |
190.197 |
1.94e-55 |
69.254 |
| HMC |
10 |
211.207 |
7.89e-58 |
75.109 |
| HMC |
15 |
204.415 |
7.68e-42 |
122.262 |
| HMC |
30 |
208.776 |
1.26e-39 |
145.646 |
| SMC |
2 |
-0.701 |
0.488 |
-0.220 |
| SMC |
5 |
0.946 |
0.35 |
0.314 |
| SMC |
10 |
0.738 |
0.465 |
0.234 |
| SMC |
15 |
1.215 |
0.234 |
0.577 |
| SMC |
30 |
-0.050 |
0.961 |
-0.021 |
| Metro |
2 |
17.061 |
4.87e-13 |
61.044 |
| Metro |
5 |
13.422 |
3.57e-11 |
60.706 |
| Metro |
10 |
16.420 |
1e-12 |
67.335 |
| Metro |
15 |
13.509 |
3.34e-11 |
106.687 |
| Metro |
30 |
80.291 |
3.66e-26 |
143.223 |
| DEMetro_Z |
2 |
5.681 |
1.76e-05 |
39.922 |
| DEMetro_Z |
5 |
15.809 |
2.01e-12 |
73.466 |
| DEMetro_Z |
10 |
12.481 |
1.33e-10 |
344.591 |
| DEMetro_Z |
15 |
17.818 |
2.57e-13 |
747.161 |
| DEMetro_Z |
30 |
20.390 |
2.24e-14 |
1555.508 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
3.699
|
0.00152
|
0.827
|
| HMC_vs_DEMetro_Z |
1
|
-0.908
|
0.375
|
-0.203
|
| HMC_vs_DEMetro_Z |
2
|
-9.732
|
8.14e-09
|
-2.176
|
| HMC_vs_DEMetro_Z |
3
|
-14.840
|
6.65e-12
|
-3.318
|
| HMC_vs_DEMetro_Z |
4
|
-18.500
|
1.31e-13
|
-4.137
|
| Metro_vs_SMC |
0
|
17.377
|
4.03e-13
|
3.886
|
| Metro_vs_SMC |
1
|
13.333
|
4.29e-11
|
2.981
|
| Metro_vs_SMC |
2
|
16.308
|
1.25e-12
|
3.647
|
| Metro_vs_SMC |
3
|
13.277
|
4.61e-11
|
2.969
|
| Metro_vs_SMC |
4
|
80.209
|
1.63e-25
|
17.935
|
| Metro_vs_DEMetro_Z |
0
|
2.829
|
0.0107
|
0.633
|
| Metro_vs_DEMetro_Z |
1
|
-2.775
|
0.0121
|
-0.620
|
| Metro_vs_DEMetro_Z |
2
|
-10.097
|
4.5e-09
|
-2.258
|
| Metro_vs_DEMetro_Z |
3
|
-15.018
|
5.39e-12
|
-3.358
|
| Metro_vs_DEMetro_Z |
4
|
-18.405
|
1.44e-13
|
-4.115
|
| HMC_vs_Metro |
0
|
1.366
|
0.188
|
0.305
|
| HMC_vs_Metro |
1
|
1.895
|
0.0734
|
0.424
|
| HMC_vs_Metro |
2
|
1.920
|
0.0699
|
0.429
|
| HMC_vs_Metro |
3
|
2.020
|
0.0578
|
0.452
|
| HMC_vs_Metro |
4
|
1.419
|
0.172
|
0.317
|
| HMC_vs_SMC |
0
|
156.552
|
5.05e-31
|
35.006
|
| HMC_vs_SMC |
1
|
240.797
|
1.42e-34
|
53.844
|
| HMC_vs_SMC |
2
|
190.852
|
1.17e-32
|
42.676
|
| HMC_vs_SMC |
3
|
154.056
|
6.85e-31
|
34.448
|
| HMC_vs_SMC |
4
|
183.717
|
2.42e-32
|
41.080
|
| DEMetro_Z_vs_SMC |
0
|
5.709
|
1.67e-05
|
1.277
|
| DEMetro_Z_vs_SMC |
1
|
15.693
|
2.48e-12
|
3.509
|
| DEMetro_Z_vs_SMC |
2
|
12.443
|
1.4e-10
|
2.782
|
| DEMetro_Z_vs_SMC |
3
|
17.792
|
2.64e-13
|
3.978
|
| DEMetro_Z_vs_SMC |
4
|
20.408
|
2.21e-14
|
4.563
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
4.226 |
0.090 |
0.063 |
65.947 |
| HMC |
5 |
2.692 |
0.053 |
0.038 |
69.254 |
| HMC |
10 |
1.892 |
0.044 |
0.025 |
75.109 |
| HMC |
15 |
1.546 |
0.036 |
0.012 |
122.262 |
| HMC |
30 |
1.092 |
0.032 |
0.007 |
145.646 |
| SMC |
2 |
0.076 |
0.090 |
0.063 |
-0.220 |
| SMC |
5 |
0.065 |
0.053 |
0.038 |
0.314 |
| SMC |
10 |
0.049 |
0.044 |
0.025 |
0.234 |
| SMC |
15 |
0.043 |
0.036 |
0.012 |
0.577 |
| SMC |
30 |
0.032 |
0.032 |
0.007 |
-0.021 |
| Metro |
2 |
3.919 |
0.090 |
0.063 |
61.044 |
| Metro |
5 |
2.366 |
0.053 |
0.038 |
60.706 |
| Metro |
10 |
1.700 |
0.044 |
0.025 |
67.335 |
| Metro |
15 |
1.353 |
0.036 |
0.012 |
106.687 |
| Metro |
30 |
1.075 |
0.032 |
0.007 |
143.223 |
| DEMetro_Z |
2 |
2.594 |
0.090 |
0.063 |
39.922 |
| DEMetro_Z |
5 |
2.852 |
0.053 |
0.038 |
73.466 |
| DEMetro_Z |
10 |
8.522 |
0.044 |
0.025 |
344.591 |
| DEMetro_Z |
15 |
9.260 |
0.036 |
0.012 |
747.161 |
| DEMetro_Z |
30 |
11.354 |
0.032 |
0.007 |
1555.508 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
643.357 |
5.51e-77 |
219.494 |
| HMC |
5 |
704.742 |
8.24e-80 |
221.169 |
| HMC |
10 |
614.225 |
1.73e-54 |
357.528 |
| HMC |
15 |
644.972 |
8.6e-69 |
263.366 |
| HMC |
30 |
697.483 |
2.22e-65 |
312.559 |
| SMC |
2 |
0.110 |
0.913 |
0.029 |
| SMC |
5 |
-0.865 |
0.394 |
-0.228 |
| SMC |
10 |
1.856 |
0.0714 |
0.643 |
| SMC |
15 |
0.169 |
0.867 |
0.058 |
| SMC |
30 |
-1.338 |
0.189 |
-0.416 |
| Metro |
2 |
14.204 |
1.42e-11 |
199.259 |
| Metro |
5 |
10.866 |
1.35e-09 |
186.363 |
| Metro |
10 |
12.276 |
1.76e-10 |
305.653 |
| Metro |
15 |
10.539 |
2.24e-09 |
218.630 |
| Metro |
30 |
49.448 |
1.39e-21 |
303.396 |
| DEMetro_Z |
2 |
5.291 |
4.17e-05 |
126.767 |
| DEMetro_Z |
5 |
6.680 |
2.19e-06 |
254.436 |
| DEMetro_Z |
10 |
11.101 |
9.54e-10 |
743.207 |
| DEMetro_Z |
15 |
12.378 |
1.53e-10 |
758.119 |
| DEMetro_Z |
30 |
15.997 |
1.76e-12 |
1014.149 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
737.286
|
8.31e-44
|
164.862
|
| HMC_vs_SMC |
1
|
906.600
|
1.64e-45
|
202.722
|
| HMC_vs_SMC |
2
|
627.792
|
1.76e-42
|
140.379
|
| HMC_vs_SMC |
3
|
793.478
|
2.06e-44
|
177.427
|
| HMC_vs_SMC |
4
|
914.637
|
1.38e-45
|
204.519
|
| Metro_vs_DEMetro_Z |
0
|
2.694
|
0.0144
|
0.602
|
| Metro_vs_DEMetro_Z |
1
|
-1.868
|
0.0772
|
-0.418
|
| Metro_vs_DEMetro_Z |
2
|
-6.749
|
1.9e-06
|
-1.509
|
| Metro_vs_DEMetro_Z |
3
|
-7.457
|
4.68e-07
|
-1.668
|
| Metro_vs_DEMetro_Z |
4
|
-11.145
|
8.93e-10
|
-2.492
|
| HMC_vs_Metro |
0
|
1.451
|
0.163
|
0.324
|
| HMC_vs_Metro |
1
|
2.028
|
0.0568
|
0.453
|
| HMC_vs_Metro |
2
|
2.093
|
0.05
|
0.468
|
| HMC_vs_Metro |
3
|
2.154
|
0.0443
|
0.482
|
| HMC_vs_Metro |
4
|
1.468
|
0.158
|
0.328
|
| HMC_vs_DEMetro_Z |
0
|
3.874
|
0.00102
|
0.866
|
| HMC_vs_DEMetro_Z |
1
|
-0.873
|
0.394
|
-0.195
|
| HMC_vs_DEMetro_Z |
2
|
-5.757
|
1.51e-05
|
-1.287
|
| HMC_vs_DEMetro_Z |
3
|
-8.075
|
1.46e-07
|
-1.806
|
| HMC_vs_DEMetro_Z |
4
|
-11.045
|
1.04e-09
|
-2.470
|
| Metro_vs_SMC |
0
|
14.209
|
1.42e-11
|
3.177
|
| Metro_vs_SMC |
1
|
10.870
|
1.35e-09
|
2.431
|
| Metro_vs_SMC |
2
|
12.280
|
1.75e-10
|
2.746
|
| Metro_vs_SMC |
3
|
10.483
|
2.45e-09
|
2.344
|
| Metro_vs_SMC |
4
|
49.801
|
1.34e-21
|
11.136
|
| DEMetro_Z_vs_SMC |
0
|
5.282
|
4.25e-05
|
1.181
|
| DEMetro_Z_vs_SMC |
1
|
6.693
|
2.13e-06
|
1.497
|
| DEMetro_Z_vs_SMC |
2
|
11.094
|
9.64e-10
|
2.481
|
| DEMetro_Z_vs_SMC |
3
|
12.380
|
1.53e-10
|
2.768
|
| DEMetro_Z_vs_SMC |
4
|
15.989
|
1.78e-12
|
3.575
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
25.451 |
0.121 |
0.115 |
219.494 |
| HMC |
5 |
16.096 |
0.091 |
0.072 |
221.169 |
| HMC |
10 |
11.374 |
0.070 |
0.032 |
357.528 |
| HMC |
15 |
9.283 |
0.067 |
0.035 |
263.366 |
| HMC |
30 |
6.570 |
0.056 |
0.021 |
312.559 |
| SMC |
2 |
0.124 |
0.121 |
0.115 |
0.029 |
| SMC |
5 |
0.075 |
0.091 |
0.072 |
-0.228 |
| SMC |
10 |
0.090 |
0.070 |
0.032 |
0.643 |
| SMC |
15 |
0.070 |
0.067 |
0.035 |
0.058 |
| SMC |
30 |
0.047 |
0.056 |
0.021 |
-0.416 |
| Metro |
2 |
23.116 |
0.121 |
0.115 |
199.259 |
| Metro |
5 |
13.577 |
0.091 |
0.072 |
186.363 |
| Metro |
10 |
9.734 |
0.070 |
0.032 |
305.653 |
| Metro |
15 |
7.718 |
0.067 |
0.035 |
218.630 |
| Metro |
30 |
6.379 |
0.056 |
0.021 |
303.396 |
| DEMetro_Z |
2 |
14.750 |
0.121 |
0.115 |
126.767 |
| DEMetro_Z |
5 |
18.504 |
0.091 |
0.072 |
254.436 |
| DEMetro_Z |
10 |
23.568 |
0.070 |
0.032 |
743.207 |
| DEMetro_Z |
15 |
26.595 |
0.067 |
0.035 |
758.119 |
| DEMetro_Z |
30 |
21.193 |
0.056 |
0.021 |
1014.149 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
53.435 |
3.35e-23 |
69.187 |
| HMC |
5 |
40.196 |
2.47e-20 |
69.759 |
| HMC |
10 |
59.687 |
5.44e-24 |
84.236 |
| HMC |
15 |
79.607 |
5.45e-26 |
154.477 |
| HMC |
30 |
81.149 |
5.29e-26 |
184.720 |
| SMC |
2 |
-0.877 |
0.386 |
-0.263 |
| SMC |
5 |
0.502 |
0.619 |
0.153 |
| SMC |
10 |
0.717 |
0.478 |
0.229 |
| SMC |
15 |
1.235 |
0.227 |
0.596 |
| SMC |
30 |
0.102 |
0.919 |
0.045 |
| Metro |
2 |
16.036 |
1.53e-12 |
65.963 |
| Metro |
5 |
13.222 |
4.64e-11 |
60.684 |
| Metro |
10 |
16.088 |
1.48e-12 |
77.564 |
| Metro |
15 |
13.126 |
5.54e-11 |
133.667 |
| Metro |
30 |
55.746 |
1.12e-22 |
186.353 |
| DEMetro_Z |
2 |
5.676 |
1.79e-05 |
44.051 |
| DEMetro_Z |
5 |
16.051 |
1.56e-12 |
82.015 |
| DEMetro_Z |
10 |
13.288 |
4.54e-11 |
419.126 |
| DEMetro_Z |
15 |
17.739 |
2.78e-13 |
994.365 |
| DEMetro_Z |
30 |
21.984 |
5.67e-15 |
2086.007 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
2.670
|
0.0151
|
0.597
|
| Metro_vs_DEMetro_Z |
1
|
-4.037
|
0.000704
|
-0.903
|
| Metro_vs_DEMetro_Z |
2
|
-10.790
|
1.53e-09
|
-2.413
|
| Metro_vs_DEMetro_Z |
3
|
-15.128
|
4.74e-12
|
-3.383
|
| Metro_vs_DEMetro_Z |
4
|
-19.800
|
3.82e-14
|
-4.427
|
| DEMetro_Z_vs_SMC |
0
|
5.707
|
1.68e-05
|
1.276
|
| DEMetro_Z_vs_SMC |
1
|
16.033
|
1.7e-12
|
3.585
|
| DEMetro_Z_vs_SMC |
2
|
13.265
|
4.68e-11
|
2.966
|
| DEMetro_Z_vs_SMC |
3
|
17.718
|
2.85e-13
|
3.962
|
| DEMetro_Z_vs_SMC |
4
|
21.999
|
5.6e-15
|
4.919
|
| HMC_vs_DEMetro_Z |
0
|
3.086
|
0.00608
|
0.690
|
| HMC_vs_DEMetro_Z |
1
|
-2.190
|
0.0412
|
-0.490
|
| HMC_vs_DEMetro_Z |
2
|
-10.673
|
1.83e-09
|
-2.386
|
| HMC_vs_DEMetro_Z |
3
|
-14.814
|
6.85e-12
|
-3.313
|
| HMC_vs_DEMetro_Z |
4
|
-19.954
|
3.32e-14
|
-4.462
|
| HMC_vs_Metro |
0
|
0.712
|
0.485
|
0.159
|
| HMC_vs_Metro |
1
|
2.091
|
0.0502
|
0.467
|
| HMC_vs_Metro |
2
|
1.487
|
0.153
|
0.333
|
| HMC_vs_Metro |
3
|
2.079
|
0.0514
|
0.465
|
| HMC_vs_Metro |
4
|
-0.452
|
0.656
|
-0.101
|
| HMC_vs_SMC |
0
|
52.095
|
5.73e-22
|
11.649
|
| HMC_vs_SMC |
1
|
40.691
|
6.02e-20
|
9.099
|
| HMC_vs_SMC |
2
|
57.706
|
8.31e-23
|
12.903
|
| HMC_vs_SMC |
3
|
81.002
|
1.36e-25
|
18.113
|
| HMC_vs_SMC |
4
|
82.107
|
1.05e-25
|
18.360
|
| Metro_vs_SMC |
0
|
16.318
|
1.24e-12
|
3.649
|
| Metro_vs_SMC |
1
|
13.244
|
4.82e-11
|
2.961
|
| Metro_vs_SMC |
2
|
16.050
|
1.67e-12
|
3.589
|
| Metro_vs_SMC |
3
|
12.949
|
7.09e-11
|
2.896
|
| Metro_vs_SMC |
4
|
54.603
|
2.36e-22
|
12.210
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
3.781 |
0.099 |
0.053 |
69.187 |
| HMC |
5 |
2.215 |
0.061 |
0.031 |
69.759 |
| HMC |
10 |
1.513 |
0.050 |
0.017 |
84.236 |
| HMC |
15 |
1.250 |
0.044 |
0.008 |
154.477 |
| HMC |
30 |
0.870 |
0.039 |
0.004 |
184.720 |
| SMC |
2 |
0.085 |
0.099 |
0.053 |
-0.263 |
| SMC |
5 |
0.066 |
0.061 |
0.031 |
0.153 |
| SMC |
10 |
0.054 |
0.050 |
0.017 |
0.229 |
| SMC |
15 |
0.049 |
0.044 |
0.008 |
0.596 |
| SMC |
30 |
0.039 |
0.039 |
0.004 |
0.045 |
| Metro |
2 |
3.610 |
0.099 |
0.053 |
65.963 |
| Metro |
5 |
1.935 |
0.061 |
0.031 |
60.684 |
| Metro |
10 |
1.397 |
0.050 |
0.017 |
77.564 |
| Metro |
15 |
1.088 |
0.044 |
0.008 |
133.667 |
| Metro |
30 |
0.877 |
0.039 |
0.004 |
186.353 |
| DEMetro_Z |
2 |
2.444 |
0.099 |
0.053 |
44.051 |
| DEMetro_Z |
5 |
2.593 |
0.061 |
0.031 |
82.015 |
| DEMetro_Z |
10 |
7.327 |
0.050 |
0.017 |
419.126 |
| DEMetro_Z |
15 |
7.810 |
0.044 |
0.008 |
994.365 |
| DEMetro_Z |
30 |
9.422 |
0.039 |
0.004 |
2086.007 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
130.607 |
5.03e-37 |
77.892 |
| HMC |
5 |
125.468 |
1.23e-36 |
74.602 |
| HMC |
10 |
176.031 |
3.78e-45 |
84.638 |
| HMC |
15 |
135.760 |
5.13e-32 |
146.691 |
| HMC |
30 |
130.344 |
7.15e-31 |
175.605 |
| SMC |
2 |
-0.501 |
0.619 |
-0.166 |
| SMC |
5 |
0.825 |
0.414 |
0.267 |
| SMC |
10 |
0.671 |
0.506 |
0.212 |
| SMC |
15 |
1.346 |
0.189 |
0.658 |
| SMC |
30 |
0.067 |
0.947 |
0.029 |
| Metro |
2 |
17.456 |
3.34e-13 |
72.730 |
| Metro |
5 |
13.559 |
3.02e-11 |
65.674 |
| Metro |
10 |
16.522 |
9.14e-13 |
75.343 |
| Metro |
15 |
13.414 |
3.81e-11 |
130.233 |
| Metro |
30 |
66.221 |
3.23e-24 |
170.881 |
| DEMetro_Z |
2 |
5.750 |
1.52e-05 |
48.403 |
| DEMetro_Z |
5 |
20.746 |
1.28e-14 |
61.159 |
| DEMetro_Z |
10 |
41.599 |
2.77e-20 |
127.923 |
| DEMetro_Z |
15 |
76.929 |
2.35e-25 |
251.636 |
| DEMetro_Z |
30 |
43.158 |
1.9e-20 |
367.497 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.770
|
1.47e-05
|
1.290
|
| DEMetro_Z_vs_SMC |
1
|
20.736
|
1.65e-14
|
4.637
|
| DEMetro_Z_vs_SMC |
2
|
40.771
|
5.8e-20
|
9.117
|
| DEMetro_Z_vs_SMC |
3
|
72.733
|
1.04e-24
|
16.264
|
| DEMetro_Z_vs_SMC |
4
|
43.617
|
1.63e-20
|
9.753
|
| HMC_vs_Metro |
0
|
1.227
|
0.235
|
0.274
|
| HMC_vs_Metro |
1
|
1.772
|
0.0924
|
0.396
|
| HMC_vs_Metro |
2
|
2.033
|
0.0563
|
0.455
|
| HMC_vs_Metro |
3
|
1.696
|
0.106
|
0.379
|
| HMC_vs_Metro |
4
|
1.602
|
0.126
|
0.358
|
| Metro_vs_DEMetro_Z |
0
|
2.730
|
0.0133
|
0.610
|
| Metro_vs_DEMetro_Z |
1
|
0.859
|
0.401
|
0.192
|
| Metro_vs_DEMetro_Z |
2
|
-8.860
|
3.56e-08
|
-1.981
|
| Metro_vs_DEMetro_Z |
3
|
-12.761
|
9.1e-11
|
-2.854
|
| Metro_vs_DEMetro_Z |
4
|
-21.077
|
1.22e-14
|
-4.713
|
| HMC_vs_SMC |
0
|
114.037
|
2.07e-28
|
25.499
|
| HMC_vs_SMC |
1
|
116.069
|
1.48e-28
|
25.954
|
| HMC_vs_SMC |
2
|
173.083
|
7.51e-32
|
38.703
|
| HMC_vs_SMC |
3
|
129.817
|
1.77e-29
|
29.028
|
| HMC_vs_SMC |
4
|
126.424
|
2.92e-29
|
28.269
|
| Metro_vs_SMC |
0
|
17.729
|
2.81e-13
|
3.964
|
| Metro_vs_SMC |
1
|
13.476
|
3.56e-11
|
3.013
|
| Metro_vs_SMC |
2
|
16.478
|
1.04e-12
|
3.685
|
| Metro_vs_SMC |
3
|
13.178
|
5.25e-11
|
2.947
|
| Metro_vs_SMC |
4
|
67.616
|
4.15e-24
|
15.119
|
| HMC_vs_DEMetro_Z |
0
|
3.470
|
0.00256
|
0.776
|
| HMC_vs_DEMetro_Z |
1
|
4.830
|
0.000116
|
1.080
|
| HMC_vs_DEMetro_Z |
2
|
-14.118
|
1.59e-11
|
-3.157
|
| HMC_vs_DEMetro_Z |
3
|
-26.365
|
1.99e-16
|
-5.895
|
| HMC_vs_DEMetro_Z |
4
|
-22.851
|
2.79e-15
|
-5.110
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.614 |
0.013 |
0.008 |
77.892 |
| HMC |
5 |
0.599 |
0.012 |
0.008 |
74.602 |
| HMC |
10 |
0.561 |
0.014 |
0.006 |
84.638 |
| HMC |
15 |
0.528 |
0.013 |
0.004 |
146.691 |
| HMC |
30 |
0.458 |
0.014 |
0.003 |
175.605 |
| SMC |
2 |
0.012 |
0.013 |
0.008 |
-0.166 |
| SMC |
5 |
0.014 |
0.012 |
0.008 |
0.267 |
| SMC |
10 |
0.015 |
0.014 |
0.006 |
0.212 |
| SMC |
15 |
0.016 |
0.013 |
0.004 |
0.658 |
| SMC |
30 |
0.014 |
0.014 |
0.003 |
0.029 |
| Metro |
2 |
0.574 |
0.013 |
0.008 |
72.730 |
| Metro |
5 |
0.529 |
0.012 |
0.008 |
65.674 |
| Metro |
10 |
0.501 |
0.014 |
0.006 |
75.343 |
| Metro |
15 |
0.470 |
0.013 |
0.004 |
130.233 |
| Metro |
30 |
0.446 |
0.014 |
0.003 |
170.881 |
| DEMetro_Z |
2 |
0.386 |
0.013 |
0.008 |
48.403 |
| DEMetro_Z |
5 |
0.493 |
0.012 |
0.008 |
61.159 |
| DEMetro_Z |
10 |
0.841 |
0.014 |
0.006 |
127.923 |
| DEMetro_Z |
15 |
0.896 |
0.013 |
0.004 |
251.636 |
| DEMetro_Z |
30 |
0.942 |
0.014 |
0.003 |
367.497 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_heavy_Tails_and_high_correlation
(MvStudentT,
dimension,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.131 |
0.896 |
0.037 |
| HMC |
5 |
2.429 |
0.0216 |
1.159 |
| HMC |
10 |
1.764 |
0.0917 |
1.505 |
| HMC |
15 |
3.594 |
0.00141 |
2.185 |
| HMC |
30 |
4.108 |
0.000549 |
5.924 |
| SMC |
2 |
2.523 |
0.0167 |
1.033 |
| SMC |
5 |
7.022 |
1.07e-06 |
33.637 |
| SMC |
10 |
8.622 |
4.57e-08 |
18.623 |
| SMC |
15 |
5.945 |
1e-05 |
53.656 |
| SMC |
30 |
38.681 |
1.49e-19 |
336.521 |
| Metro |
2 |
1.892 |
0.0733 |
3.251 |
| Metro |
5 |
7.032 |
9.36e-07 |
14.151 |
| Metro |
10 |
3.241 |
0.00427 |
11.946 |
| Metro |
15 |
4.351 |
0.000344 |
139.579 |
| Metro |
30 |
4.059 |
0.00067 |
739.086 |
| DEMetro_Z |
2 |
2.751 |
0.0102 |
1.322 |
| DEMetro_Z |
5 |
4.438 |
0.000282 |
339.261 |
| DEMetro_Z |
10 |
6.562 |
2.77e-06 |
100.019 |
| DEMetro_Z |
15 |
6.316 |
4.62e-06 |
494.912 |
| DEMetro_Z |
30 |
10.415 |
2.72e-09 |
1257.395 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.768
|
0.0123
|
-0.619
|
| HMC_vs_DEMetro_Z |
1
|
-4.418
|
0.000295
|
-0.988
|
| HMC_vs_DEMetro_Z |
2
|
-6.381
|
4.03e-06
|
-1.427
|
| HMC_vs_DEMetro_Z |
3
|
-6.282
|
4.96e-06
|
-1.405
|
| HMC_vs_DEMetro_Z |
4
|
-10.318
|
3.17e-09
|
-2.307
|
| Metro_vs_SMC |
0
|
1.190
|
0.249
|
0.266
|
| Metro_vs_SMC |
1
|
-4.711
|
0.000152
|
-1.053
|
| Metro_vs_SMC |
2
|
-1.544
|
0.139
|
-0.345
|
| Metro_vs_SMC |
3
|
2.785
|
0.0118
|
0.623
|
| Metro_vs_SMC |
4
|
2.204
|
0.0401
|
0.493
|
| Metro_vs_DEMetro_Z |
0
|
1.129
|
0.273
|
0.253
|
| Metro_vs_DEMetro_Z |
1
|
-4.259
|
0.000424
|
-0.952
|
| Metro_vs_DEMetro_Z |
2
|
-5.887
|
1.14e-05
|
-1.316
|
| Metro_vs_DEMetro_Z |
3
|
-4.181
|
0.000507
|
-0.935
|
| Metro_vs_DEMetro_Z |
4
|
-2.072
|
0.0521
|
-0.463
|
| HMC_vs_Metro |
0
|
-1.817
|
0.0851
|
-0.406
|
| HMC_vs_Metro |
1
|
-6.576
|
2.7e-06
|
-1.470
|
| HMC_vs_Metro |
2
|
-3.021
|
0.00702
|
-0.676
|
| HMC_vs_Metro |
3
|
-4.310
|
0.000377
|
-0.964
|
| HMC_vs_Metro |
4
|
-4.040
|
0.0007
|
-0.903
|
| HMC_vs_SMC |
0
|
-3.591
|
0.00195
|
-0.803
|
| HMC_vs_SMC |
1
|
-6.683
|
2.17e-06
|
-1.494
|
| HMC_vs_SMC |
2
|
-7.062
|
1.01e-06
|
-1.579
|
| HMC_vs_SMC |
3
|
-5.823
|
1.31e-05
|
-1.302
|
| HMC_vs_SMC |
4
|
-36.086
|
5.74e-19
|
-8.069
|
| DEMetro_Z_vs_SMC |
0
|
0.504
|
0.62
|
0.113
|
| DEMetro_Z_vs_SMC |
1
|
4.028
|
0.000718
|
0.901
|
| DEMetro_Z_vs_SMC |
2
|
4.925
|
9.4e-05
|
1.101
|
| DEMetro_Z_vs_SMC |
3
|
5.694
|
1.73e-05
|
1.273
|
| DEMetro_Z_vs_SMC |
4
|
7.570
|
3.77e-07
|
1.693
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.069 |
0.067 |
0.049 |
0.037 |
| HMC |
5 |
0.092 |
0.052 |
0.035 |
1.159 |
| HMC |
10 |
0.247 |
0.082 |
0.109 |
1.505 |
| HMC |
15 |
0.139 |
0.056 |
0.038 |
2.185 |
| HMC |
30 |
0.286 |
0.062 |
0.038 |
5.924 |
| SMC |
2 |
0.117 |
0.067 |
0.049 |
1.033 |
| SMC |
5 |
1.215 |
0.052 |
0.035 |
33.637 |
| SMC |
10 |
2.120 |
0.082 |
0.109 |
18.623 |
| SMC |
15 |
2.117 |
0.056 |
0.038 |
53.656 |
| SMC |
30 |
12.789 |
0.062 |
0.038 |
336.521 |
| Metro |
2 |
0.225 |
0.067 |
0.049 |
3.251 |
| Metro |
5 |
0.542 |
0.052 |
0.035 |
14.151 |
| Metro |
10 |
1.389 |
0.082 |
0.109 |
11.946 |
| Metro |
15 |
5.417 |
0.056 |
0.038 |
139.579 |
| Metro |
30 |
28.013 |
0.062 |
0.038 |
739.086 |
| DEMetro_Z |
2 |
0.131 |
0.067 |
0.049 |
1.322 |
| DEMetro_Z |
5 |
11.785 |
0.052 |
0.035 |
339.261 |
| DEMetro_Z |
10 |
11.026 |
0.082 |
0.109 |
100.019 |
| DEMetro_Z |
15 |
19.066 |
0.056 |
0.038 |
494.912 |
| DEMetro_Z |
30 |
47.614 |
0.062 |
0.038 |
1257.395 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.007 |
0.324 |
-0.242 |
| HMC |
5 |
1.486 |
0.148 |
0.675 |
| HMC |
10 |
-0.656 |
0.518 |
-0.161 |
| HMC |
15 |
-0.099 |
0.922 |
-0.027 |
| HMC |
30 |
1.007 |
0.323 |
0.515 |
| SMC |
2 |
1.851 |
0.0742 |
0.474 |
| SMC |
5 |
22.567 |
3.46e-15 |
300.331 |
| SMC |
10 |
26.521 |
5.3e-18 |
6.135 |
| SMC |
15 |
145.779 |
5.83e-31 |
319.542 |
| SMC |
30 |
132.805 |
5.63e-30 |
372.997 |
| Metro |
2 |
0.054 |
0.957 |
0.016 |
| Metro |
5 |
1.171 |
0.249 |
0.353 |
| Metro |
10 |
-0.320 |
0.751 |
-0.082 |
| Metro |
15 |
1.409 |
0.175 |
70.849 |
| Metro |
30 |
2.223 |
0.0385 |
664.387 |
| DEMetro_Z |
2 |
-0.775 |
0.446 |
-0.183 |
| DEMetro_Z |
5 |
3.678 |
0.0016 |
462.934 |
| DEMetro_Z |
10 |
6.160 |
7.44e-07 |
2.651 |
| DEMetro_Z |
15 |
5.445 |
2.97e-05 |
148.367 |
| DEMetro_Z |
30 |
13.798 |
2.35e-11 |
178.019 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-4.571
|
0.000209
|
-1.022
|
| HMC_vs_SMC |
1
|
-22.368
|
4.13e-15
|
-5.002
|
| HMC_vs_SMC |
2
|
-52.021
|
5.89e-22
|
-11.632
|
| HMC_vs_SMC |
3
|
-146.746
|
1.72e-30
|
-32.813
|
| HMC_vs_SMC |
4
|
-121.894
|
5.84e-29
|
-27.256
|
| Metro_vs_DEMetro_Z |
0
|
1.056
|
0.304
|
0.236
|
| Metro_vs_DEMetro_Z |
1
|
-3.676
|
0.0016
|
-0.822
|
| Metro_vs_DEMetro_Z |
2
|
-8.272
|
1.02e-07
|
-1.850
|
| Metro_vs_DEMetro_Z |
3
|
-1.376
|
0.185
|
-0.308
|
| Metro_vs_DEMetro_Z |
4
|
1.656
|
0.114
|
0.370
|
| HMC_vs_Metro |
0
|
-1.392
|
0.18
|
-0.311
|
| HMC_vs_Metro |
1
|
0.777
|
0.447
|
0.174
|
| HMC_vs_Metro |
2
|
-0.516
|
0.612
|
-0.115
|
| HMC_vs_Metro |
3
|
-1.411
|
0.174
|
-0.315
|
| HMC_vs_Metro |
4
|
-2.222
|
0.0386
|
-0.497
|
| HMC_vs_DEMetro_Z |
0
|
-2.402
|
0.0267
|
-0.537
|
| HMC_vs_DEMetro_Z |
1
|
-3.674
|
0.00161
|
-0.821
|
| HMC_vs_DEMetro_Z |
2
|
-7.104
|
9.33e-07
|
-1.589
|
| HMC_vs_DEMetro_Z |
3
|
-5.436
|
3.03e-05
|
-1.216
|
| HMC_vs_DEMetro_Z |
4
|
-13.752
|
2.51e-11
|
-3.075
|
| Metro_vs_SMC |
0
|
-1.944
|
0.0669
|
-0.435
|
| Metro_vs_SMC |
1
|
-22.436
|
3.9e-15
|
-5.017
|
| Metro_vs_SMC |
2
|
-38.894
|
1.41e-19
|
-8.697
|
| Metro_vs_SMC |
3
|
-4.980
|
8.31e-05
|
-1.114
|
| Metro_vs_SMC |
4
|
0.975
|
0.342
|
0.218
|
| DEMetro_Z_vs_SMC |
0
|
-4.255
|
0.000428
|
-0.952
|
| DEMetro_Z_vs_SMC |
1
|
1.309
|
0.206
|
0.293
|
| DEMetro_Z_vs_SMC |
2
|
-9.436
|
1.33e-08
|
-2.110
|
| DEMetro_Z_vs_SMC |
3
|
-6.465
|
3.39e-06
|
-1.446
|
| DEMetro_Z_vs_SMC |
4
|
-14.620
|
8.64e-12
|
-3.269
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
4.763 |
8.853 |
16.927 |
-0.242 |
| HMC |
5 |
7.213 |
3.438 |
5.591 |
0.675 |
| HMC |
10 |
26.639 |
61.875 |
219.151 |
-0.161 |
| HMC |
15 |
5.079 |
5.279 |
7.467 |
-0.027 |
| HMC |
30 |
17.167 |
8.067 |
17.680 |
0.515 |
| SMC |
2 |
16.879 |
8.853 |
16.927 |
0.474 |
| SMC |
5 |
1682.466 |
3.438 |
5.591 |
300.331 |
| SMC |
10 |
1406.382 |
61.875 |
219.151 |
6.135 |
| SMC |
15 |
2391.306 |
5.279 |
7.467 |
319.542 |
| SMC |
30 |
6602.712 |
8.067 |
17.680 |
372.997 |
| Metro |
2 |
9.122 |
8.853 |
16.927 |
0.016 |
| Metro |
5 |
5.411 |
3.438 |
5.591 |
0.353 |
| Metro |
10 |
43.808 |
61.875 |
219.151 |
-0.082 |
| Metro |
15 |
534.312 |
5.279 |
7.467 |
70.849 |
| Metro |
30 |
11754.532 |
8.067 |
17.680 |
664.387 |
| DEMetro_Z |
2 |
5.754 |
8.853 |
16.927 |
-0.183 |
| DEMetro_Z |
5 |
2591.513 |
3.438 |
5.591 |
462.934 |
| DEMetro_Z |
10 |
642.921 |
61.875 |
219.151 |
2.651 |
| DEMetro_Z |
15 |
1113.138 |
5.279 |
7.467 |
148.367 |
| DEMetro_Z |
30 |
3155.463 |
8.067 |
17.680 |
178.019 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.360 |
0.0237 |
0.679 |
| HMC |
5 |
5.671 |
9.99e-06 |
4.455 |
| HMC |
10 |
2.342 |
0.0287 |
1.978 |
| HMC |
15 |
7.792 |
7.71e-08 |
5.941 |
| HMC |
30 |
4.587 |
0.000199 |
20.712 |
| SMC |
2 |
8.617 |
4.77e-08 |
20.843 |
| SMC |
5 |
26.910 |
1.36e-16 |
1030.668 |
| SMC |
10 |
110.318 |
1.99e-28 |
310.459 |
| SMC |
15 |
164.049 |
1.93e-31 |
1463.582 |
| SMC |
30 |
251.600 |
5.87e-35 |
2933.622 |
| Metro |
2 |
3.772 |
0.00122 |
6.328 |
| Metro |
5 |
11.194 |
6.08e-10 |
21.481 |
| Metro |
10 |
3.019 |
0.00703 |
17.168 |
| Metro |
15 |
3.917 |
0.000926 |
261.586 |
| Metro |
30 |
6.313 |
4.65e-06 |
2313.048 |
| DEMetro_Z |
2 |
7.797 |
1.44e-08 |
3.755 |
| DEMetro_Z |
5 |
7.374 |
5.5e-07 |
804.879 |
| DEMetro_Z |
10 |
14.989 |
5.52e-12 |
187.741 |
| DEMetro_Z |
15 |
12.305 |
1.69e-10 |
1097.975 |
| DEMetro_Z |
30 |
20.686 |
1.72e-14 |
2476.134 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.513
|
0.147
|
0.338
|
| Metro_vs_DEMetro_Z |
1
|
-7.219
|
7.44e-07
|
-1.614
|
| Metro_vs_DEMetro_Z |
2
|
-15.478
|
3.17e-12
|
-3.461
|
| Metro_vs_DEMetro_Z |
3
|
-8.395
|
8.13e-08
|
-1.877
|
| Metro_vs_DEMetro_Z |
4
|
-0.420
|
0.679
|
-0.094
|
| DEMetro_Z_vs_SMC |
0
|
-6.433
|
3.63e-06
|
-1.438
|
| DEMetro_Z_vs_SMC |
1
|
-2.228
|
0.0382
|
-0.498
|
| DEMetro_Z_vs_SMC |
2
|
-9.794
|
7.35e-09
|
-2.190
|
| DEMetro_Z_vs_SMC |
3
|
-4.269
|
0.000415
|
-0.954
|
| DEMetro_Z_vs_SMC |
4
|
-3.687
|
0.00156
|
-0.824
|
| HMC_vs_DEMetro_Z |
0
|
-6.550
|
2.85e-06
|
-1.465
|
| HMC_vs_DEMetro_Z |
1
|
-7.333
|
5.96e-07
|
-1.640
|
| HMC_vs_DEMetro_Z |
2
|
-14.655
|
8.28e-12
|
-3.277
|
| HMC_vs_DEMetro_Z |
3
|
-12.234
|
1.87e-10
|
-2.736
|
| HMC_vs_DEMetro_Z |
4
|
-20.379
|
2.26e-14
|
-4.557
|
| HMC_vs_Metro |
0
|
-3.272
|
0.00401
|
-0.732
|
| HMC_vs_Metro |
1
|
-7.820
|
2.35e-07
|
-1.749
|
| HMC_vs_Metro |
2
|
-2.710
|
0.0139
|
-0.606
|
| HMC_vs_Metro |
3
|
-3.850
|
0.00108
|
-0.861
|
| HMC_vs_Metro |
4
|
-6.314
|
4.64e-06
|
-1.412
|
| HMC_vs_SMC |
0
|
-8.242
|
1.07e-07
|
-1.843
|
| HMC_vs_SMC |
1
|
-26.683
|
1.6e-16
|
-5.967
|
| HMC_vs_SMC |
2
|
-111.787
|
3.02e-28
|
-24.996
|
| HMC_vs_SMC |
3
|
-159.404
|
3.59e-31
|
-35.644
|
| HMC_vs_SMC |
4
|
-234.633
|
2.32e-34
|
-52.466
|
| Metro_vs_SMC |
0
|
-4.802
|
0.000124
|
-1.074
|
| Metro_vs_SMC |
1
|
-26.502
|
1.81e-16
|
-5.926
|
| Metro_vs_SMC |
2
|
-51.601
|
6.86e-22
|
-11.538
|
| Metro_vs_SMC |
3
|
-18.098
|
1.94e-13
|
-4.047
|
| Metro_vs_SMC |
4
|
-1.698
|
0.106
|
-0.380
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.146 |
0.119 |
0.040 |
0.679 |
| HMC |
5 |
0.215 |
0.100 |
0.026 |
4.455 |
| HMC |
10 |
0.309 |
0.133 |
0.089 |
1.978 |
| HMC |
15 |
0.246 |
0.099 |
0.025 |
5.941 |
| HMC |
30 |
0.550 |
0.105 |
0.021 |
20.712 |
| SMC |
2 |
0.946 |
0.119 |
0.040 |
20.843 |
| SMC |
5 |
26.585 |
0.100 |
0.026 |
1030.668 |
| SMC |
10 |
27.697 |
0.133 |
0.089 |
310.459 |
| SMC |
15 |
36.307 |
0.099 |
0.025 |
1463.582 |
| SMC |
30 |
63.156 |
0.105 |
0.021 |
2933.622 |
| Metro |
2 |
0.370 |
0.119 |
0.040 |
6.328 |
| Metro |
5 |
0.652 |
0.100 |
0.026 |
21.481 |
| Metro |
10 |
1.657 |
0.133 |
0.089 |
17.168 |
| Metro |
15 |
6.570 |
0.099 |
0.025 |
261.586 |
| Metro |
30 |
49.818 |
0.105 |
0.021 |
2313.048 |
| DEMetro_Z |
2 |
0.268 |
0.119 |
0.040 |
3.755 |
| DEMetro_Z |
5 |
20.783 |
0.100 |
0.026 |
804.879 |
| DEMetro_Z |
10 |
16.802 |
0.133 |
0.089 |
187.741 |
| DEMetro_Z |
15 |
27.262 |
0.099 |
0.025 |
1097.975 |
| DEMetro_Z |
30 |
53.323 |
0.105 |
0.021 |
2476.134 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.535 |
0.00116 |
1.307 |
| HMC |
5 |
3.911 |
0.000772 |
3.472 |
| HMC |
10 |
5.216 |
4.47e-05 |
9.527 |
| HMC |
15 |
7.362 |
3.44e-07 |
8.223 |
| HMC |
30 |
6.470 |
3.14e-06 |
17.697 |
| SMC |
2 |
10.538 |
1.99e-09 |
31.142 |
| SMC |
5 |
130.781 |
4.49e-32 |
130.268 |
| SMC |
10 |
118.609 |
1.87e-29 |
214.854 |
| SMC |
15 |
114.956 |
1.36e-30 |
122.239 |
| SMC |
30 |
130.787 |
9.63e-35 |
92.519 |
| Metro |
2 |
7.850 |
1.46e-07 |
10.023 |
| Metro |
5 |
8.752 |
4.03e-08 |
30.788 |
| Metro |
10 |
10.979 |
1.12e-09 |
76.202 |
| Metro |
15 |
17.767 |
2.56e-13 |
103.145 |
| Metro |
30 |
31.665 |
5.78e-18 |
147.763 |
| DEMetro_Z |
2 |
7.215 |
3.11e-07 |
5.925 |
| DEMetro_Z |
5 |
34.056 |
1.29e-18 |
112.991 |
| DEMetro_Z |
10 |
44.734 |
8.91e-21 |
234.997 |
| DEMetro_Z |
15 |
25.861 |
2.67e-16 |
159.974 |
| DEMetro_Z |
30 |
31.433 |
6.64e-18 |
146.524 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-7.899
|
2.02e-07
|
-1.766
|
| DEMetro_Z_vs_SMC |
1
|
-5.837
|
1.27e-05
|
-1.305
|
| DEMetro_Z_vs_SMC |
2
|
3.397
|
0.00302
|
0.760
|
| DEMetro_Z_vs_SMC |
3
|
5.965
|
9.68e-06
|
1.334
|
| DEMetro_Z_vs_SMC |
4
|
11.630
|
4.39e-10
|
2.601
|
| HMC_vs_Metro |
0
|
-6.428
|
3.66e-06
|
-1.437
|
| HMC_vs_Metro |
1
|
-7.997
|
1.69e-07
|
-1.788
|
| HMC_vs_Metro |
2
|
-8.963
|
2.98e-08
|
-2.004
|
| HMC_vs_Metro |
3
|
-15.844
|
2.09e-12
|
-3.543
|
| HMC_vs_Metro |
4
|
-25.127
|
4.85e-16
|
-5.619
|
| Metro_vs_DEMetro_Z |
0
|
2.847
|
0.0103
|
0.637
|
| Metro_vs_DEMetro_Z |
1
|
-20.869
|
1.47e-14
|
-4.666
|
| Metro_vs_DEMetro_Z |
2
|
-17.554
|
3.36e-13
|
-3.925
|
| Metro_vs_DEMetro_Z |
3
|
-6.256
|
5.23e-06
|
-1.399
|
| Metro_vs_DEMetro_Z |
4
|
0.201
|
0.843
|
0.045
|
| HMC_vs_SMC |
0
|
-9.956
|
5.65e-09
|
-2.226
|
| HMC_vs_SMC |
1
|
-115.709
|
1.57e-28
|
-25.873
|
| HMC_vs_SMC |
2
|
-84.177
|
6.54e-26
|
-18.822
|
| HMC_vs_SMC |
3
|
-86.916
|
3.57e-26
|
-19.435
|
| HMC_vs_SMC |
4
|
-24.891
|
5.77e-16
|
-5.566
|
| Metro_vs_SMC |
0
|
-6.450
|
3.5e-06
|
-1.442
|
| Metro_vs_SMC |
1
|
-28.732
|
4.04e-17
|
-6.425
|
| Metro_vs_SMC |
2
|
-19.706
|
4.17e-14
|
-4.406
|
| Metro_vs_SMC |
3
|
-3.180
|
0.00493
|
-0.711
|
| Metro_vs_SMC |
4
|
11.767
|
3.61e-10
|
2.631
|
| HMC_vs_DEMetro_Z |
0
|
-5.380
|
3.42e-05
|
-1.203
|
| HMC_vs_DEMetro_Z |
1
|
-34.187
|
1.58e-18
|
-7.644
|
| HMC_vs_DEMetro_Z |
2
|
-40.178
|
7.64e-20
|
-8.984
|
| HMC_vs_DEMetro_Z |
3
|
-25.121
|
4.87e-16
|
-5.617
|
| HMC_vs_DEMetro_Z |
4
|
-21.441
|
8.96e-15
|
-4.794
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.021 |
0.014 |
0.005 |
1.307 |
| HMC |
5 |
0.031 |
0.016 |
0.005 |
3.472 |
| HMC |
10 |
0.041 |
0.015 |
0.003 |
9.527 |
| HMC |
15 |
0.050 |
0.015 |
0.004 |
8.223 |
| HMC |
30 |
0.095 |
0.015 |
0.005 |
17.697 |
| SMC |
2 |
0.175 |
0.014 |
0.005 |
31.142 |
| SMC |
5 |
0.605 |
0.016 |
0.005 |
130.268 |
| SMC |
10 |
0.600 |
0.015 |
0.003 |
214.854 |
| SMC |
15 |
0.539 |
0.015 |
0.004 |
122.239 |
| SMC |
30 |
0.433 |
0.015 |
0.005 |
92.519 |
| Metro |
2 |
0.066 |
0.014 |
0.005 |
10.023 |
| Metro |
5 |
0.155 |
0.016 |
0.005 |
30.788 |
| Metro |
10 |
0.222 |
0.015 |
0.003 |
76.202 |
| Metro |
15 |
0.457 |
0.015 |
0.004 |
103.145 |
| Metro |
30 |
0.682 |
0.015 |
0.005 |
147.763 |
| DEMetro_Z |
2 |
0.045 |
0.014 |
0.005 |
5.925 |
| DEMetro_Z |
5 |
0.527 |
0.016 |
0.005 |
112.991 |
| DEMetro_Z |
10 |
0.655 |
0.015 |
0.003 |
234.997 |
| DEMetro_Z |
15 |
0.701 |
0.015 |
0.004 |
159.974 |
| DEMetro_Z |
30 |
0.677 |
0.015 |
0.005 |
146.524 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.540 |
0.133 |
0.592 |
| HMC |
5 |
1.860 |
0.0734 |
0.920 |
| HMC |
10 |
0.532 |
0.599 |
0.141 |
| HMC |
15 |
2.560 |
0.0187 |
3.749 |
| HMC |
30 |
3.827 |
0.00109 |
6.874 |
| SMC |
2 |
1.376 |
0.178 |
0.552 |
| SMC |
5 |
4.885 |
0.000102 |
40.365 |
| SMC |
10 |
9.906 |
4.57e-09 |
18.075 |
| SMC |
15 |
7.633 |
3.26e-07 |
38.753 |
| SMC |
30 |
27.408 |
9.35e-17 |
230.483 |
| Metro |
2 |
3.932 |
0.000752 |
3.726 |
| Metro |
5 |
3.618 |
0.00182 |
13.766 |
| Metro |
10 |
5.642 |
1.58e-05 |
7.531 |
| Metro |
15 |
4.794 |
0.000126 |
56.462 |
| Metro |
30 |
5.951 |
9.97e-06 |
633.994 |
| DEMetro_Z |
2 |
3.099 |
0.0043 |
1.480 |
| DEMetro_Z |
5 |
3.669 |
0.00163 |
173.897 |
| DEMetro_Z |
10 |
5.044 |
7.19e-05 |
47.477 |
| DEMetro_Z |
15 |
5.699 |
1.71e-05 |
425.392 |
| DEMetro_Z |
30 |
6.948 |
1.27e-06 |
1499.400 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.866
|
0.0775
|
-0.417
|
| HMC_vs_DEMetro_Z |
1
|
-3.638
|
0.00175
|
-0.814
|
| HMC_vs_DEMetro_Z |
2
|
-5.004
|
7.89e-05
|
-1.119
|
| HMC_vs_DEMetro_Z |
3
|
-5.642
|
1.93e-05
|
-1.262
|
| HMC_vs_DEMetro_Z |
4
|
-6.915
|
1.36e-06
|
-1.546
|
| Metro_vs_SMC |
0
|
3.352
|
0.00335
|
0.750
|
| Metro_vs_SMC |
1
|
-2.591
|
0.0179
|
-0.579
|
| Metro_vs_SMC |
2
|
-5.245
|
4.61e-05
|
-1.173
|
| Metro_vs_SMC |
3
|
1.292
|
0.212
|
0.289
|
| Metro_vs_SMC |
4
|
3.693
|
0.00155
|
0.826
|
| Metro_vs_DEMetro_Z |
0
|
1.955
|
0.0655
|
0.437
|
| Metro_vs_DEMetro_Z |
1
|
-3.350
|
0.00337
|
-0.749
|
| Metro_vs_DEMetro_Z |
2
|
-4.194
|
0.000492
|
-0.938
|
| Metro_vs_DEMetro_Z |
3
|
-5.002
|
7.91e-05
|
-1.119
|
| Metro_vs_DEMetro_Z |
4
|
-3.676
|
0.00161
|
-0.822
|
| HMC_vs_Metro |
0
|
-3.806
|
0.00119
|
-0.851
|
| HMC_vs_Metro |
1
|
-3.407
|
0.00296
|
-0.762
|
| HMC_vs_Metro |
2
|
-5.897
|
1.12e-05
|
-1.319
|
| HMC_vs_Metro |
3
|
-4.395
|
0.000311
|
-0.983
|
| HMC_vs_Metro |
4
|
-5.876
|
1.17e-05
|
-1.314
|
| HMC_vs_SMC |
0
|
0.081
|
0.936
|
0.018
|
| HMC_vs_SMC |
1
|
-4.803
|
0.000124
|
-1.074
|
| HMC_vs_SMC |
2
|
-10.068
|
4.72e-09
|
-2.251
|
| HMC_vs_SMC |
3
|
-7.013
|
1.12e-06
|
-1.568
|
| HMC_vs_SMC |
4
|
-26.334
|
2.04e-16
|
-5.889
|
| DEMetro_Z_vs_SMC |
0
|
1.457
|
0.161
|
0.326
|
| DEMetro_Z_vs_SMC |
1
|
2.699
|
0.0142
|
0.603
|
| DEMetro_Z_vs_SMC |
2
|
3.152
|
0.00525
|
0.705
|
| DEMetro_Z_vs_SMC |
3
|
5.198
|
5.12e-05
|
1.162
|
| DEMetro_Z_vs_SMC |
4
|
5.971
|
9.54e-06
|
1.335
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.096 |
0.067 |
0.049 |
0.592 |
| HMC |
5 |
0.084 |
0.052 |
0.035 |
0.920 |
| HMC |
10 |
0.097 |
0.082 |
0.109 |
0.141 |
| HMC |
15 |
0.200 |
0.056 |
0.038 |
3.749 |
| HMC |
30 |
0.322 |
0.062 |
0.038 |
6.874 |
| SMC |
2 |
0.094 |
0.067 |
0.049 |
0.552 |
| SMC |
5 |
1.448 |
0.052 |
0.035 |
40.365 |
| SMC |
10 |
2.060 |
0.082 |
0.109 |
18.075 |
| SMC |
15 |
1.544 |
0.056 |
0.038 |
38.753 |
| SMC |
30 |
8.778 |
0.062 |
0.038 |
230.483 |
| Metro |
2 |
0.249 |
0.067 |
0.049 |
3.726 |
| Metro |
5 |
0.528 |
0.052 |
0.035 |
13.766 |
| Metro |
10 |
0.906 |
0.082 |
0.109 |
7.531 |
| Metro |
15 |
2.224 |
0.056 |
0.038 |
56.462 |
| Metro |
30 |
24.038 |
0.062 |
0.038 |
633.994 |
| DEMetro_Z |
2 |
0.139 |
0.067 |
0.049 |
1.480 |
| DEMetro_Z |
5 |
6.066 |
0.052 |
0.035 |
173.897 |
| DEMetro_Z |
10 |
5.277 |
0.082 |
0.109 |
47.477 |
| DEMetro_Z |
15 |
16.396 |
0.056 |
0.038 |
425.392 |
| DEMetro_Z |
30 |
56.766 |
0.062 |
0.038 |
1499.400 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-0.972 |
0.341 |
-0.230 |
| HMC |
5 |
1.289 |
0.205 |
0.425 |
| HMC |
10 |
-1.108 |
0.282 |
-0.248 |
| HMC |
15 |
0.803 |
0.429 |
0.410 |
| HMC |
30 |
0.620 |
0.54 |
0.318 |
| SMC |
2 |
-0.003 |
0.998 |
-0.001 |
| SMC |
5 |
18.742 |
1.02e-13 |
241.697 |
| SMC |
10 |
21.462 |
1.71e-20 |
5.654 |
| SMC |
15 |
83.795 |
5.22e-26 |
326.561 |
| SMC |
30 |
72.483 |
9.27e-25 |
358.053 |
| Metro |
2 |
-0.566 |
0.576 |
-0.135 |
| Metro |
5 |
1.199 |
0.245 |
2.086 |
| Metro |
10 |
-1.134 |
0.271 |
-0.254 |
| Metro |
15 |
2.175 |
0.0424 |
10.234 |
| Metro |
30 |
2.333 |
0.0308 |
87.834 |
| DEMetro_Z |
2 |
-0.750 |
0.461 |
-0.180 |
| DEMetro_Z |
5 |
1.732 |
0.0994 |
270.100 |
| DEMetro_Z |
10 |
2.149 |
0.038 |
0.664 |
| DEMetro_Z |
15 |
3.809 |
0.00118 |
52.221 |
| DEMetro_Z |
30 |
8.828 |
3.64e-08 |
43.461 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-2.113
|
0.048
|
-0.473
|
| HMC_vs_SMC |
1
|
-18.770
|
1.01e-13
|
-4.197
|
| HMC_vs_SMC |
2
|
-42.130
|
3.13e-20
|
-9.421
|
| HMC_vs_SMC |
3
|
-82.310
|
1e-25
|
-18.405
|
| HMC_vs_SMC |
4
|
-71.151
|
1.58e-24
|
-15.910
|
| Metro_vs_DEMetro_Z |
0
|
0.866
|
0.398
|
0.194
|
| Metro_vs_DEMetro_Z |
1
|
-1.719
|
0.102
|
-0.384
|
| Metro_vs_DEMetro_Z |
2
|
-4.292
|
0.000394
|
-0.960
|
| Metro_vs_DEMetro_Z |
3
|
-2.937
|
0.00847
|
-0.657
|
| Metro_vs_DEMetro_Z |
4
|
1.153
|
0.263
|
0.258
|
| HMC_vs_Metro |
0
|
-2.115
|
0.0478
|
-0.473
|
| HMC_vs_Metro |
1
|
-0.964
|
0.347
|
-0.216
|
| HMC_vs_Metro |
2
|
0.624
|
0.54
|
0.140
|
| HMC_vs_Metro |
3
|
-2.080
|
0.0513
|
-0.465
|
| HMC_vs_Metro |
4
|
-2.324
|
0.0314
|
-0.520
|
| HMC_vs_DEMetro_Z |
0
|
-2.579
|
0.0184
|
-0.577
|
| HMC_vs_DEMetro_Z |
1
|
-1.730
|
0.0999
|
-0.387
|
| HMC_vs_DEMetro_Z |
2
|
-4.236
|
0.000447
|
-0.947
|
| HMC_vs_DEMetro_Z |
3
|
-3.749
|
0.00136
|
-0.838
|
| HMC_vs_DEMetro_Z |
4
|
-8.605
|
5.58e-08
|
-1.924
|
| Metro_vs_SMC |
0
|
-1.432
|
0.168
|
-0.320
|
| Metro_vs_SMC |
1
|
-17.992
|
2.16e-13
|
-4.023
|
| Metro_vs_SMC |
2
|
-42.065
|
3.22e-20
|
-9.406
|
| Metro_vs_SMC |
3
|
-58.153
|
7.18e-23
|
-13.003
|
| Metro_vs_SMC |
4
|
-6.900
|
1.4e-06
|
-1.543
|
| DEMetro_Z_vs_SMC |
0
|
-1.588
|
0.129
|
-0.355
|
| DEMetro_Z_vs_SMC |
1
|
0.181
|
0.858
|
0.040
|
| DEMetro_Z_vs_SMC |
2
|
-24.856
|
5.92e-16
|
-5.558
|
| DEMetro_Z_vs_SMC |
3
|
-20.600
|
1.86e-14
|
-4.606
|
| DEMetro_Z_vs_SMC |
4
|
-45.547
|
7.22e-21
|
-10.185
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
4.965 |
8.853 |
16.927 |
-0.230 |
| HMC |
5 |
5.817 |
3.438 |
5.591 |
0.425 |
| HMC |
10 |
7.536 |
61.875 |
219.151 |
-0.248 |
| HMC |
15 |
8.339 |
5.279 |
7.467 |
0.410 |
| HMC |
30 |
13.690 |
8.067 |
17.680 |
0.318 |
| SMC |
2 |
8.842 |
8.853 |
16.927 |
-0.001 |
| SMC |
5 |
1354.669 |
3.438 |
5.591 |
241.697 |
| SMC |
10 |
1301.003 |
61.875 |
219.151 |
5.654 |
| SMC |
15 |
2443.717 |
5.279 |
7.467 |
326.561 |
| SMC |
30 |
6338.502 |
8.067 |
17.680 |
358.053 |
| Metro |
2 |
6.576 |
8.853 |
16.927 |
-0.135 |
| Metro |
5 |
15.103 |
3.438 |
5.591 |
2.086 |
| Metro |
10 |
6.267 |
61.875 |
219.151 |
-0.254 |
| Metro |
15 |
81.698 |
5.279 |
7.467 |
10.234 |
| Metro |
30 |
1560.983 |
8.067 |
17.680 |
87.834 |
| DEMetro_Z |
2 |
5.813 |
8.853 |
16.927 |
-0.180 |
| DEMetro_Z |
5 |
1513.458 |
3.438 |
5.591 |
270.100 |
| DEMetro_Z |
10 |
207.394 |
61.875 |
219.151 |
0.664 |
| DEMetro_Z |
15 |
395.213 |
5.279 |
7.467 |
52.221 |
| DEMetro_Z |
30 |
776.459 |
8.067 |
17.680 |
43.461 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.985 |
0.00031 |
1.411 |
| HMC |
5 |
4.493 |
0.000211 |
5.205 |
| HMC |
10 |
3.310 |
0.00223 |
1.308 |
| HMC |
15 |
4.760 |
0.000127 |
9.170 |
| HMC |
30 |
3.435 |
0.00277 |
21.899 |
| SMC |
2 |
5.219 |
4.56e-05 |
11.168 |
| SMC |
5 |
25.102 |
4.93e-16 |
918.302 |
| SMC |
10 |
66.652 |
4.35e-24 |
291.968 |
| SMC |
15 |
88.023 |
2.76e-26 |
1478.330 |
| SMC |
30 |
139.415 |
4.5e-30 |
2855.314 |
| Metro |
2 |
6.378 |
2.64e-06 |
6.668 |
| Metro |
5 |
3.175 |
0.00497 |
26.685 |
| Metro |
10 |
7.353 |
3.83e-07 |
9.066 |
| Metro |
15 |
5.261 |
4.45e-05 |
111.172 |
| Metro |
30 |
5.316 |
3.94e-05 |
1135.589 |
| DEMetro_Z |
2 |
6.709 |
2.66e-07 |
3.306 |
| DEMetro_Z |
5 |
3.489 |
0.00246 |
365.123 |
| DEMetro_Z |
10 |
6.799 |
1.71e-06 |
87.526 |
| DEMetro_Z |
15 |
8.312 |
9.46e-08 |
731.363 |
| DEMetro_Z |
30 |
8.063 |
1.49e-07 |
2373.284 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
2.763
|
0.0124
|
0.618
|
| Metro_vs_DEMetro_Z |
1
|
-3.186
|
0.00487
|
-0.712
|
| Metro_vs_DEMetro_Z |
2
|
-6.019
|
8.62e-06
|
-1.346
|
| Metro_vs_DEMetro_Z |
3
|
-7.154
|
8.45e-07
|
-1.600
|
| Metro_vs_DEMetro_Z |
4
|
-3.250
|
0.00421
|
-0.727
|
| DEMetro_Z_vs_SMC |
0
|
-3.411
|
0.00293
|
-0.763
|
| DEMetro_Z_vs_SMC |
1
|
-4.970
|
8.51e-05
|
-1.111
|
| DEMetro_Z_vs_SMC |
2
|
-16.465
|
1.06e-12
|
-3.682
|
| DEMetro_Z_vs_SMC |
3
|
-8.276
|
1.01e-07
|
-1.851
|
| DEMetro_Z_vs_SMC |
4
|
-1.679
|
0.109
|
-0.375
|
| HMC_vs_DEMetro_Z |
0
|
-3.623
|
0.00181
|
-0.810
|
| HMC_vs_DEMetro_Z |
1
|
-3.439
|
0.00275
|
-0.769
|
| HMC_vs_DEMetro_Z |
2
|
-6.653
|
2.31e-06
|
-1.488
|
| HMC_vs_DEMetro_Z |
3
|
-8.133
|
1.31e-07
|
-1.819
|
| HMC_vs_DEMetro_Z |
4
|
-7.981
|
1.73e-07
|
-1.785
|
| HMC_vs_Metro |
0
|
-5.094
|
6.45e-05
|
-1.139
|
| HMC_vs_Metro |
1
|
-2.602
|
0.0175
|
-0.582
|
| HMC_vs_Metro |
2
|
-7.137
|
8.75e-07
|
-1.596
|
| HMC_vs_Metro |
3
|
-4.727
|
0.000147
|
-1.057
|
| HMC_vs_Metro |
4
|
-5.242
|
4.64e-05
|
-1.172
|
| HMC_vs_SMC |
0
|
-4.714
|
0.000151
|
-1.054
|
| HMC_vs_SMC |
1
|
-24.780
|
6.27e-16
|
-5.541
|
| HMC_vs_SMC |
2
|
-66.351
|
5.93e-24
|
-14.836
|
| HMC_vs_SMC |
3
|
-88.602
|
2.48e-26
|
-19.812
|
| HMC_vs_SMC |
4
|
-138.581
|
5.11e-30
|
-30.988
|
| Metro_vs_SMC |
0
|
-2.169
|
0.043
|
-0.485
|
| Metro_vs_SMC |
1
|
-22.830
|
2.84e-15
|
-5.105
|
| Metro_vs_SMC |
2
|
-63.848
|
1.23e-23
|
-14.277
|
| Metro_vs_SMC |
3
|
-50.862
|
9.01e-22
|
-11.373
|
| Metro_vs_SMC |
4
|
-7.776
|
2.55e-07
|
-1.739
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.175 |
0.119 |
0.040 |
1.411 |
| HMC |
5 |
0.234 |
0.100 |
0.026 |
5.205 |
| HMC |
10 |
0.249 |
0.133 |
0.089 |
1.308 |
| HMC |
15 |
0.326 |
0.099 |
0.025 |
9.170 |
| HMC |
30 |
0.575 |
0.105 |
0.021 |
21.899 |
| SMC |
2 |
0.562 |
0.119 |
0.040 |
11.168 |
| SMC |
5 |
23.698 |
0.100 |
0.026 |
918.302 |
| SMC |
10 |
26.056 |
0.133 |
0.089 |
291.968 |
| SMC |
15 |
36.672 |
0.099 |
0.025 |
1478.330 |
| SMC |
30 |
61.473 |
0.105 |
0.021 |
2855.314 |
| Metro |
2 |
0.383 |
0.119 |
0.040 |
6.668 |
| Metro |
5 |
0.786 |
0.100 |
0.026 |
26.685 |
| Metro |
10 |
0.938 |
0.133 |
0.089 |
9.066 |
| Metro |
15 |
2.849 |
0.099 |
0.025 |
111.172 |
| Metro |
30 |
24.511 |
0.105 |
0.021 |
1135.589 |
| DEMetro_Z |
2 |
0.250 |
0.119 |
0.040 |
3.306 |
| DEMetro_Z |
5 |
9.483 |
0.100 |
0.026 |
365.123 |
| DEMetro_Z |
10 |
7.904 |
0.133 |
0.089 |
87.526 |
| DEMetro_Z |
15 |
18.192 |
0.099 |
0.025 |
731.363 |
| DEMetro_Z |
30 |
51.113 |
0.105 |
0.021 |
2373.284 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
4.094 |
0.000347 |
2.163 |
| HMC |
5 |
5.414 |
1.94e-05 |
4.452 |
| HMC |
10 |
4.574 |
0.000199 |
10.703 |
| HMC |
15 |
7.127 |
6.04e-07 |
8.699 |
| HMC |
30 |
3.591 |
0.00195 |
25.852 |
| SMC |
2 |
7.189 |
7.4e-07 |
21.942 |
| SMC |
5 |
90.253 |
1.71e-27 |
131.698 |
| SMC |
10 |
115.216 |
3.74e-29 |
217.125 |
| SMC |
15 |
83.060 |
1.07e-26 |
126.456 |
| SMC |
30 |
167.108 |
4.85e-41 |
92.885 |
| Metro |
2 |
8.933 |
1.86e-08 |
11.308 |
| Metro |
5 |
7.480 |
4.34e-07 |
32.508 |
| Metro |
10 |
6.942 |
1.28e-06 |
82.426 |
| Metro |
15 |
10.792 |
1.5e-09 |
105.305 |
| Metro |
30 |
26.482 |
1.73e-16 |
174.479 |
| DEMetro_Z |
2 |
10.540 |
1.12e-11 |
4.710 |
| DEMetro_Z |
5 |
9.169 |
2.07e-08 |
84.759 |
| DEMetro_Z |
10 |
20.983 |
1.3e-14 |
193.005 |
| DEMetro_Z |
15 |
19.636 |
4.34e-14 |
180.147 |
| DEMetro_Z |
30 |
20.500 |
1.98e-14 |
183.916 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-5.709
|
1.67e-05
|
-1.277
|
| DEMetro_Z_vs_SMC |
1
|
-4.995
|
8.04e-05
|
-1.117
|
| DEMetro_Z_vs_SMC |
2
|
-2.459
|
0.0237
|
-0.550
|
| DEMetro_Z_vs_SMC |
3
|
5.872
|
1.18e-05
|
1.313
|
| DEMetro_Z_vs_SMC |
4
|
10.227
|
3.66e-09
|
2.287
|
| HMC_vs_Metro |
0
|
-7.490
|
4.4e-07
|
-1.675
|
| HMC_vs_Metro |
1
|
-6.972
|
1.21e-06
|
-1.559
|
| HMC_vs_Metro |
2
|
-5.969
|
9.6e-06
|
-1.335
|
| HMC_vs_Metro |
3
|
-9.648
|
9.34e-09
|
-2.157
|
| HMC_vs_Metro |
4
|
-15.394
|
3.48e-12
|
-3.442
|
| Metro_vs_DEMetro_Z |
0
|
4.814
|
0.000121
|
1.076
|
| Metro_vs_DEMetro_Z |
1
|
-4.944
|
9.01e-05
|
-1.106
|
| Metro_vs_DEMetro_Z |
2
|
-6.292
|
4.86e-06
|
-1.407
|
| Metro_vs_DEMetro_Z |
3
|
-4.684
|
0.000162
|
-1.047
|
| Metro_vs_DEMetro_Z |
4
|
-0.859
|
0.401
|
-0.192
|
| HMC_vs_SMC |
0
|
-6.897
|
1.41e-06
|
-1.542
|
| HMC_vs_SMC |
1
|
-71.040
|
1.63e-24
|
-15.885
|
| HMC_vs_SMC |
2
|
-73.092
|
9.5e-25
|
-16.344
|
| HMC_vs_SMC |
3
|
-78.074
|
2.72e-25
|
-17.458
|
| HMC_vs_SMC |
4
|
-9.219
|
1.92e-08
|
-2.061
|
| Metro_vs_SMC |
0
|
-3.590
|
0.00195
|
-0.803
|
| Metro_vs_SMC |
1
|
-19.410
|
5.48e-14
|
-4.340
|
| Metro_vs_SMC |
2
|
-11.667
|
4.16e-10
|
-2.609
|
| Metro_vs_SMC |
3
|
-2.039
|
0.0556
|
-0.456
|
| Metro_vs_SMC |
4
|
12.684
|
1.01e-10
|
2.836
|
| HMC_vs_DEMetro_Z |
0
|
-3.958
|
0.000843
|
-0.885
|
| HMC_vs_DEMetro_Z |
1
|
-8.471
|
7.1e-08
|
-1.894
|
| HMC_vs_DEMetro_Z |
2
|
-18.944
|
8.52e-14
|
-4.236
|
| HMC_vs_DEMetro_Z |
3
|
-19.054
|
7.67e-14
|
-4.261
|
| HMC_vs_DEMetro_Z |
4
|
-14.320
|
1.24e-11
|
-3.202
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.025 |
0.014 |
0.005 |
2.163 |
| HMC |
5 |
0.036 |
0.016 |
0.005 |
4.452 |
| HMC |
10 |
0.044 |
0.015 |
0.003 |
10.703 |
| HMC |
15 |
0.052 |
0.015 |
0.004 |
8.699 |
| HMC |
30 |
0.131 |
0.015 |
0.005 |
25.852 |
| SMC |
2 |
0.127 |
0.014 |
0.005 |
21.942 |
| SMC |
5 |
0.611 |
0.016 |
0.005 |
131.698 |
| SMC |
10 |
0.606 |
0.015 |
0.003 |
217.125 |
| SMC |
15 |
0.557 |
0.015 |
0.004 |
126.456 |
| SMC |
30 |
0.434 |
0.015 |
0.005 |
92.885 |
| Metro |
2 |
0.073 |
0.014 |
0.005 |
11.308 |
| Metro |
5 |
0.163 |
0.016 |
0.005 |
32.508 |
| Metro |
10 |
0.239 |
0.015 |
0.003 |
82.426 |
| Metro |
15 |
0.467 |
0.015 |
0.004 |
105.305 |
| Metro |
30 |
0.803 |
0.015 |
0.005 |
174.479 |
| DEMetro_Z |
2 |
0.039 |
0.014 |
0.005 |
4.710 |
| DEMetro_Z |
5 |
0.399 |
0.016 |
0.005 |
84.759 |
| DEMetro_Z |
10 |
0.541 |
0.015 |
0.003 |
193.005 |
| DEMetro_Z |
15 |
0.788 |
0.015 |
0.004 |
180.147 |
| DEMetro_Z |
30 |
0.846 |
0.015 |
0.005 |
183.916 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_only_Mode_distance
(Mixture,
mm,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.569 |
0.000161 |
4.248 |
| HMC |
8 |
5.056 |
6.96e-05 |
31.189 |
| HMC |
10 |
4.929 |
9.21e-05 |
23.032 |
| HMC |
12 |
3.783 |
0.00125 |
20.146 |
| HMC |
15 |
4.033 |
0.000707 |
24.978 |
| HMC |
18 |
6.007 |
8.72e-06 |
32.634 |
| SMC |
5 |
-1.149 |
0.258 |
-0.330 |
| SMC |
8 |
1.050 |
0.301 |
0.425 |
| SMC |
10 |
1.455 |
0.154 |
0.442 |
| SMC |
12 |
0.802 |
0.428 |
0.250 |
| SMC |
15 |
0.187 |
0.853 |
0.061 |
| SMC |
18 |
-0.998 |
0.325 |
-0.286 |
| Metro |
5 |
3.262 |
0.003 |
1.717 |
| Metro |
8 |
7.017 |
1.02e-06 |
18.327 |
| Metro |
10 |
6.223 |
5.47e-06 |
26.832 |
| Metro |
12 |
4.166 |
0.000521 |
22.274 |
| Metro |
15 |
4.067 |
0.000654 |
25.160 |
| Metro |
18 |
6.086 |
7.38e-06 |
34.401 |
| DEMetro_Z |
5 |
2.780 |
0.00898 |
1.149 |
| DEMetro_Z |
8 |
6.431 |
3.46e-06 |
20.096 |
| DEMetro_Z |
10 |
4.829 |
0.000113 |
14.129 |
| DEMetro_Z |
12 |
4.531 |
0.000223 |
13.915 |
| DEMetro_Z |
15 |
4.674 |
0.000164 |
24.305 |
| DEMetro_Z |
18 |
6.675 |
2.15e-06 |
30.800 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
3.248
|
0.00423
|
0.726
|
| HMC_vs_DEMetro_Z |
1
|
1.328
|
0.2
|
0.297
|
| HMC_vs_DEMetro_Z |
2
|
1.711
|
0.103
|
0.383
|
| HMC_vs_DEMetro_Z |
3
|
1.119
|
0.277
|
0.250
|
| HMC_vs_DEMetro_Z |
4
|
0.111
|
0.913
|
0.025
|
| HMC_vs_DEMetro_Z |
5
|
0.329
|
0.746
|
0.074
|
| Metro_vs_SMC |
0
|
3.818
|
0.00116
|
0.854
|
| Metro_vs_SMC |
1
|
6.873
|
1.48e-06
|
1.537
|
| Metro_vs_SMC |
2
|
6.131
|
6.81e-06
|
1.371
|
| Metro_vs_SMC |
3
|
4.152
|
0.000541
|
0.928
|
| Metro_vs_SMC |
4
|
4.064
|
0.000662
|
0.909
|
| Metro_vs_SMC |
5
|
6.160
|
6.4e-06
|
1.378
|
| Metro_vs_DEMetro_Z |
0
|
1.012
|
0.324
|
0.226
|
| Metro_vs_DEMetro_Z |
1
|
-0.445
|
0.662
|
-0.099
|
| Metro_vs_DEMetro_Z |
2
|
2.611
|
0.0172
|
0.584
|
| Metro_vs_DEMetro_Z |
3
|
1.609
|
0.124
|
0.360
|
| Metro_vs_DEMetro_Z |
4
|
0.150
|
0.882
|
0.034
|
| Metro_vs_DEMetro_Z |
5
|
0.615
|
0.546
|
0.138
|
| HMC_vs_Metro |
0
|
2.346
|
0.03
|
0.525
|
| HMC_vs_Metro |
1
|
1.892
|
0.0738
|
0.423
|
| HMC_vs_Metro |
2
|
-0.567
|
0.577
|
-0.127
|
| HMC_vs_Metro |
3
|
-0.680
|
0.504
|
-0.152
|
| HMC_vs_Metro |
4
|
-0.056
|
0.956
|
-0.012
|
| HMC_vs_Metro |
5
|
-0.598
|
0.557
|
-0.134
|
| HMC_vs_SMC |
0
|
5.320
|
3.91e-05
|
1.190
|
| HMC_vs_SMC |
1
|
4.972
|
8.47e-05
|
1.112
|
| HMC_vs_SMC |
2
|
4.844
|
0.000113
|
1.083
|
| HMC_vs_SMC |
3
|
3.758
|
0.00133
|
0.840
|
| HMC_vs_SMC |
4
|
4.022
|
0.000729
|
0.899
|
| HMC_vs_SMC |
5
|
6.091
|
7.41e-06
|
1.362
|
| DEMetro_Z_vs_SMC |
0
|
3.388
|
0.00309
|
0.758
|
| DEMetro_Z_vs_SMC |
1
|
6.233
|
5.49e-06
|
1.394
|
| DEMetro_Z_vs_SMC |
2
|
4.748
|
0.00014
|
1.062
|
| DEMetro_Z_vs_SMC |
3
|
4.505
|
0.000242
|
1.007
|
| DEMetro_Z_vs_SMC |
4
|
4.623
|
0.000185
|
1.034
|
| DEMetro_Z_vs_SMC |
5
|
6.723
|
2e-06
|
1.503
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.180 |
0.045 |
0.032 |
4.248 |
| HMC |
8 |
0.978 |
0.051 |
0.030 |
31.189 |
| HMC |
10 |
1.173 |
0.054 |
0.049 |
23.032 |
| HMC |
12 |
1.505 |
0.089 |
0.070 |
20.146 |
| HMC |
15 |
1.510 |
0.086 |
0.057 |
24.978 |
| HMC |
18 |
3.204 |
0.128 |
0.094 |
32.634 |
| SMC |
5 |
0.035 |
0.045 |
0.032 |
-0.330 |
| SMC |
8 |
0.064 |
0.051 |
0.030 |
0.425 |
| SMC |
10 |
0.076 |
0.054 |
0.049 |
0.442 |
| SMC |
12 |
0.107 |
0.089 |
0.070 |
0.250 |
| SMC |
15 |
0.089 |
0.086 |
0.057 |
0.061 |
| SMC |
18 |
0.101 |
0.128 |
0.094 |
-0.286 |
| Metro |
5 |
0.100 |
0.045 |
0.032 |
1.717 |
| Metro |
8 |
0.596 |
0.051 |
0.030 |
18.327 |
| Metro |
10 |
1.358 |
0.054 |
0.049 |
26.832 |
| Metro |
12 |
1.654 |
0.089 |
0.070 |
22.274 |
| Metro |
15 |
1.521 |
0.086 |
0.057 |
25.160 |
| Metro |
18 |
3.370 |
0.128 |
0.094 |
34.401 |
| DEMetro_Z |
5 |
0.082 |
0.045 |
0.032 |
1.149 |
| DEMetro_Z |
8 |
0.649 |
0.051 |
0.030 |
20.096 |
| DEMetro_Z |
10 |
0.741 |
0.054 |
0.049 |
14.129 |
| DEMetro_Z |
12 |
1.067 |
0.089 |
0.070 |
13.915 |
| DEMetro_Z |
15 |
1.472 |
0.086 |
0.057 |
24.305 |
| DEMetro_Z |
18 |
3.031 |
0.128 |
0.094 |
30.800 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.882 |
0.00688 |
1.158 |
| HMC |
8 |
2.889 |
0.0094 |
29.112 |
| HMC |
10 |
3.667 |
0.00164 |
40.058 |
| HMC |
12 |
3.128 |
0.00554 |
64.473 |
| HMC |
15 |
3.110 |
0.00577 |
60.472 |
| HMC |
18 |
4.359 |
0.000338 |
150.045 |
| SMC |
5 |
0.428 |
0.671 |
0.116 |
| SMC |
8 |
1.056 |
0.298 |
0.295 |
| SMC |
10 |
0.397 |
0.693 |
0.131 |
| SMC |
12 |
-0.987 |
0.33 |
-0.293 |
| SMC |
15 |
-1.057 |
0.297 |
-0.310 |
| SMC |
18 |
0.821 |
0.418 |
0.320 |
| Metro |
5 |
3.036 |
0.00468 |
1.245 |
| Metro |
8 |
4.255 |
0.000404 |
7.851 |
| Metro |
10 |
3.956 |
0.000845 |
48.051 |
| Metro |
12 |
3.463 |
0.0026 |
69.948 |
| Metro |
15 |
3.070 |
0.00631 |
59.656 |
| Metro |
18 |
4.519 |
0.000235 |
164.941 |
| DEMetro_Z |
5 |
3.516 |
0.00158 |
1.861 |
| DEMetro_Z |
8 |
4.432 |
0.000275 |
10.232 |
| DEMetro_Z |
10 |
2.583 |
0.0182 |
15.217 |
| DEMetro_Z |
12 |
2.137 |
0.0458 |
25.513 |
| DEMetro_Z |
15 |
2.521 |
0.0208 |
48.308 |
| DEMetro_Z |
18 |
4.314 |
0.000374 |
125.419 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.165
|
0.0051
|
0.708
|
| HMC_vs_SMC |
1
|
2.857
|
0.0101
|
0.639
|
| HMC_vs_SMC |
2
|
3.656
|
0.00168
|
0.818
|
| HMC_vs_SMC |
3
|
3.151
|
0.00527
|
0.704
|
| HMC_vs_SMC |
4
|
3.137
|
0.00543
|
0.701
|
| HMC_vs_SMC |
5
|
4.342
|
0.000351
|
0.971
|
| Metro_vs_DEMetro_Z |
0
|
-0.977
|
0.341
|
-0.218
|
| Metro_vs_DEMetro_Z |
1
|
-0.780
|
0.445
|
-0.174
|
| Metro_vs_DEMetro_Z |
2
|
2.940
|
0.0084
|
0.658
|
| Metro_vs_DEMetro_Z |
3
|
2.532
|
0.0203
|
0.566
|
| Metro_vs_DEMetro_Z |
4
|
0.538
|
0.597
|
0.120
|
| Metro_vs_DEMetro_Z |
5
|
0.919
|
0.37
|
0.205
|
| HMC_vs_Metro |
0
|
-0.165
|
0.87
|
-0.037
|
| HMC_vs_Metro |
1
|
2.038
|
0.0558
|
0.456
|
| HMC_vs_Metro |
2
|
-0.458
|
0.652
|
-0.102
|
| HMC_vs_Metro |
3
|
-0.319
|
0.753
|
-0.071
|
| HMC_vs_Metro |
4
|
0.129
|
0.899
|
0.029
|
| HMC_vs_Metro |
5
|
-0.886
|
0.387
|
-0.198
|
| HMC_vs_DEMetro_Z |
0
|
-1.183
|
0.251
|
-0.264
|
| HMC_vs_DEMetro_Z |
1
|
1.711
|
0.103
|
0.382
|
| HMC_vs_DEMetro_Z |
2
|
1.993
|
0.0609
|
0.446
|
| HMC_vs_DEMetro_Z |
3
|
1.992
|
0.0609
|
0.445
|
| HMC_vs_DEMetro_Z |
4
|
0.558
|
0.583
|
0.125
|
| HMC_vs_DEMetro_Z |
5
|
0.617
|
0.544
|
0.138
|
| Metro_vs_SMC |
0
|
2.792
|
0.0116
|
0.624
|
| Metro_vs_SMC |
1
|
4.243
|
0.00044
|
0.949
|
| Metro_vs_SMC |
2
|
3.915
|
0.000931
|
0.875
|
| Metro_vs_SMC |
3
|
3.481
|
0.0025
|
0.778
|
| Metro_vs_SMC |
4
|
3.098
|
0.00592
|
0.693
|
| Metro_vs_SMC |
5
|
4.504
|
0.000243
|
1.007
|
| DEMetro_Z_vs_SMC |
0
|
3.460
|
0.00262
|
0.774
|
| DEMetro_Z_vs_SMC |
1
|
4.271
|
0.000413
|
0.955
|
| DEMetro_Z_vs_SMC |
2
|
2.571
|
0.0187
|
0.575
|
| DEMetro_Z_vs_SMC |
3
|
2.151
|
0.0446
|
0.481
|
| DEMetro_Z_vs_SMC |
4
|
2.542
|
0.0199
|
0.568
|
| DEMetro_Z_vs_SMC |
5
|
4.296
|
0.00039
|
0.961
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.106 |
0.048 |
0.050 |
1.158 |
| HMC |
8 |
2.207 |
0.081 |
0.073 |
29.112 |
| HMC |
10 |
3.366 |
0.119 |
0.081 |
40.058 |
| HMC |
12 |
7.052 |
0.161 |
0.107 |
64.473 |
| HMC |
15 |
6.627 |
0.204 |
0.106 |
60.472 |
| HMC |
18 |
21.541 |
0.197 |
0.142 |
150.045 |
| SMC |
5 |
0.054 |
0.048 |
0.050 |
0.116 |
| SMC |
8 |
0.103 |
0.081 |
0.073 |
0.295 |
| SMC |
10 |
0.129 |
0.119 |
0.081 |
0.131 |
| SMC |
12 |
0.130 |
0.161 |
0.107 |
-0.293 |
| SMC |
15 |
0.172 |
0.204 |
0.106 |
-0.310 |
| SMC |
18 |
0.242 |
0.197 |
0.142 |
0.320 |
| Metro |
5 |
0.110 |
0.048 |
0.050 |
1.245 |
| Metro |
8 |
0.654 |
0.081 |
0.073 |
7.851 |
| Metro |
10 |
4.014 |
0.119 |
0.081 |
48.051 |
| Metro |
12 |
7.638 |
0.161 |
0.107 |
69.948 |
| Metro |
15 |
6.540 |
0.204 |
0.106 |
59.656 |
| Metro |
18 |
23.660 |
0.197 |
0.142 |
164.941 |
| DEMetro_Z |
5 |
0.141 |
0.048 |
0.050 |
1.861 |
| DEMetro_Z |
8 |
0.828 |
0.081 |
0.073 |
10.232 |
| DEMetro_Z |
10 |
1.352 |
0.119 |
0.081 |
15.217 |
| DEMetro_Z |
12 |
2.888 |
0.161 |
0.107 |
25.513 |
| DEMetro_Z |
15 |
5.335 |
0.204 |
0.106 |
48.308 |
| DEMetro_Z |
18 |
18.038 |
0.197 |
0.142 |
125.419 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.519 |
0.000191 |
4.722 |
| HMC |
8 |
5.200 |
5.07e-05 |
40.217 |
| HMC |
10 |
4.681 |
0.000162 |
27.854 |
| HMC |
12 |
3.736 |
0.00139 |
21.268 |
| HMC |
15 |
4.032 |
0.000709 |
28.597 |
| HMC |
18 |
6.024 |
8.42e-06 |
34.348 |
| SMC |
5 |
-1.412 |
0.167 |
-0.404 |
| SMC |
8 |
1.299 |
0.204 |
0.595 |
| SMC |
10 |
1.468 |
0.15 |
0.476 |
| SMC |
12 |
0.656 |
0.515 |
0.208 |
| SMC |
15 |
0.552 |
0.584 |
0.186 |
| SMC |
18 |
-0.894 |
0.378 |
-0.252 |
| Metro |
5 |
3.903 |
0.000592 |
2.139 |
| Metro |
8 |
7.035 |
1.02e-06 |
23.748 |
| Metro |
10 |
6.459 |
3.37e-06 |
32.217 |
| Metro |
12 |
4.174 |
0.000513 |
24.632 |
| Metro |
15 |
3.915 |
0.000928 |
30.246 |
| Metro |
18 |
6.065 |
7.73e-06 |
35.557 |
| DEMetro_Z |
5 |
5.578 |
2.94e-06 |
2.144 |
| DEMetro_Z |
8 |
6.588 |
2.55e-06 |
25.929 |
| DEMetro_Z |
10 |
5.006 |
7.65e-05 |
17.063 |
| DEMetro_Z |
12 |
4.368 |
0.000326 |
15.158 |
| DEMetro_Z |
15 |
4.697 |
0.000156 |
29.210 |
| DEMetro_Z |
18 |
6.703 |
2.04e-06 |
33.047 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.009
|
0.993
|
-0.002
|
| Metro_vs_DEMetro_Z |
1
|
-0.438
|
0.666
|
-0.098
|
| Metro_vs_DEMetro_Z |
2
|
2.718
|
0.0136
|
0.608
|
| Metro_vs_DEMetro_Z |
3
|
1.687
|
0.108
|
0.377
|
| Metro_vs_DEMetro_Z |
4
|
0.151
|
0.881
|
0.034
|
| Metro_vs_DEMetro_Z |
5
|
0.410
|
0.686
|
0.092
|
| DEMetro_Z_vs_SMC |
0
|
6.405
|
3.84e-06
|
1.432
|
| DEMetro_Z_vs_SMC |
1
|
6.343
|
4.37e-06
|
1.418
|
| DEMetro_Z_vs_SMC |
2
|
4.930
|
9.31e-05
|
1.102
|
| DEMetro_Z_vs_SMC |
3
|
4.350
|
0.000345
|
0.973
|
| DEMetro_Z_vs_SMC |
4
|
4.644
|
0.000177
|
1.038
|
| DEMetro_Z_vs_SMC |
5
|
6.753
|
1.88e-06
|
1.510
|
| HMC_vs_DEMetro_Z |
0
|
2.361
|
0.0291
|
0.528
|
| HMC_vs_DEMetro_Z |
1
|
1.364
|
0.188
|
0.305
|
| HMC_vs_DEMetro_Z |
2
|
1.660
|
0.113
|
0.371
|
| HMC_vs_DEMetro_Z |
3
|
1.046
|
0.309
|
0.234
|
| HMC_vs_DEMetro_Z |
4
|
-0.086
|
0.932
|
-0.019
|
| HMC_vs_DEMetro_Z |
5
|
0.224
|
0.825
|
0.050
|
| HMC_vs_Metro |
0
|
2.235
|
0.0376
|
0.500
|
| HMC_vs_Metro |
1
|
1.890
|
0.0741
|
0.423
|
| HMC_vs_Metro |
2
|
-0.520
|
0.609
|
-0.116
|
| HMC_vs_Metro |
3
|
-0.900
|
0.38
|
-0.201
|
| HMC_vs_Metro |
4
|
-0.455
|
0.654
|
-0.102
|
| HMC_vs_Metro |
5
|
-0.361
|
0.722
|
-0.081
|
| HMC_vs_SMC |
0
|
5.391
|
3.35e-05
|
1.205
|
| HMC_vs_SMC |
1
|
5.088
|
6.54e-05
|
1.138
|
| HMC_vs_SMC |
2
|
4.605
|
0.000193
|
1.030
|
| HMC_vs_SMC |
3
|
3.718
|
0.00146
|
0.831
|
| HMC_vs_SMC |
4
|
4.016
|
0.000738
|
0.898
|
| HMC_vs_SMC |
5
|
6.100
|
7.26e-06
|
1.364
|
| Metro_vs_SMC |
0
|
4.811
|
0.000121
|
1.076
|
| Metro_vs_SMC |
1
|
6.808
|
1.69e-06
|
1.522
|
| Metro_vs_SMC |
2
|
6.389
|
3.97e-06
|
1.429
|
| Metro_vs_SMC |
3
|
4.171
|
0.000519
|
0.933
|
| Metro_vs_SMC |
4
|
3.908
|
0.000945
|
0.874
|
| Metro_vs_SMC |
5
|
6.130
|
6.82e-06
|
1.371
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.169 |
0.057 |
0.024 |
4.722 |
| HMC |
8 |
0.870 |
0.060 |
0.020 |
40.217 |
| HMC |
10 |
1.068 |
0.068 |
0.036 |
27.854 |
| HMC |
12 |
1.330 |
0.097 |
0.058 |
21.268 |
| HMC |
15 |
1.355 |
0.090 |
0.044 |
28.597 |
| HMC |
18 |
2.890 |
0.132 |
0.080 |
34.348 |
| SMC |
5 |
0.047 |
0.057 |
0.024 |
-0.404 |
| SMC |
8 |
0.072 |
0.060 |
0.020 |
0.595 |
| SMC |
10 |
0.085 |
0.068 |
0.036 |
0.476 |
| SMC |
12 |
0.109 |
0.097 |
0.058 |
0.208 |
| SMC |
15 |
0.098 |
0.090 |
0.044 |
0.186 |
| SMC |
18 |
0.112 |
0.132 |
0.080 |
-0.252 |
| Metro |
5 |
0.107 |
0.057 |
0.024 |
2.139 |
| Metro |
8 |
0.538 |
0.060 |
0.020 |
23.748 |
| Metro |
10 |
1.224 |
0.068 |
0.036 |
32.217 |
| Metro |
12 |
1.525 |
0.097 |
0.058 |
24.632 |
| Metro |
15 |
1.428 |
0.090 |
0.044 |
30.246 |
| Metro |
18 |
2.987 |
0.132 |
0.080 |
35.557 |
| DEMetro_Z |
5 |
0.108 |
0.057 |
0.024 |
2.144 |
| DEMetro_Z |
8 |
0.582 |
0.060 |
0.020 |
25.929 |
| DEMetro_Z |
10 |
0.680 |
0.068 |
0.036 |
17.063 |
| DEMetro_Z |
12 |
0.975 |
0.097 |
0.058 |
15.158 |
| DEMetro_Z |
15 |
1.382 |
0.090 |
0.044 |
29.210 |
| DEMetro_Z |
18 |
2.785 |
0.132 |
0.080 |
33.047 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.713 |
0.000126 |
5.484 |
| HMC |
8 |
4.997 |
7.96e-05 |
35.557 |
| HMC |
10 |
4.937 |
9.08e-05 |
27.802 |
| HMC |
12 |
3.839 |
0.0011 |
21.237 |
| HMC |
15 |
4.083 |
0.000632 |
29.920 |
| HMC |
18 |
6.252 |
5.21e-06 |
38.047 |
| SMC |
5 |
-1.012 |
0.318 |
-0.302 |
| SMC |
8 |
0.968 |
0.34 |
0.398 |
| SMC |
10 |
1.566 |
0.126 |
0.499 |
| SMC |
12 |
0.747 |
0.46 |
0.234 |
| SMC |
15 |
0.349 |
0.729 |
0.115 |
| SMC |
18 |
-0.922 |
0.363 |
-0.273 |
| Metro |
5 |
4.004 |
0.00051 |
2.518 |
| Metro |
8 |
6.686 |
2.04e-06 |
20.476 |
| Metro |
10 |
6.273 |
4.97e-06 |
31.862 |
| Metro |
12 |
4.265 |
0.000415 |
23.307 |
| Metro |
15 |
4.112 |
0.000592 |
29.673 |
| Metro |
18 |
6.322 |
4.51e-06 |
40.626 |
| DEMetro_Z |
5 |
4.691 |
5.34e-05 |
2.081 |
| DEMetro_Z |
8 |
6.437 |
3.47e-06 |
23.426 |
| DEMetro_Z |
10 |
4.921 |
9.27e-05 |
17.216 |
| DEMetro_Z |
12 |
4.730 |
0.000142 |
14.798 |
| DEMetro_Z |
15 |
5.009 |
7.73e-05 |
29.145 |
| DEMetro_Z |
18 |
6.936 |
1.28e-06 |
36.630 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
4.814
|
0.000121
|
1.076
|
| DEMetro_Z_vs_SMC |
1
|
6.270
|
5.09e-06
|
1.402
|
| DEMetro_Z_vs_SMC |
2
|
4.833
|
0.000115
|
1.081
|
| DEMetro_Z_vs_SMC |
3
|
4.727
|
0.000147
|
1.057
|
| DEMetro_Z_vs_SMC |
4
|
4.951
|
8.87e-05
|
1.107
|
| DEMetro_Z_vs_SMC |
5
|
6.975
|
1.21e-06
|
1.560
|
| HMC_vs_Metro |
0
|
2.249
|
0.0366
|
0.503
|
| HMC_vs_Metro |
1
|
1.925
|
0.0693
|
0.431
|
| HMC_vs_Metro |
2
|
-0.505
|
0.62
|
-0.113
|
| HMC_vs_Metro |
3
|
-0.656
|
0.519
|
-0.147
|
| HMC_vs_Metro |
4
|
0.064
|
0.95
|
0.014
|
| HMC_vs_Metro |
5
|
-0.727
|
0.476
|
-0.163
|
| Metro_vs_DEMetro_Z |
0
|
0.726
|
0.477
|
0.162
|
| Metro_vs_DEMetro_Z |
1
|
-0.632
|
0.535
|
-0.141
|
| Metro_vs_DEMetro_Z |
2
|
2.561
|
0.0191
|
0.573
|
| Metro_vs_DEMetro_Z |
3
|
1.566
|
0.134
|
0.350
|
| Metro_vs_DEMetro_Z |
4
|
0.081
|
0.937
|
0.018
|
| Metro_vs_DEMetro_Z |
5
|
0.604
|
0.553
|
0.135
|
| HMC_vs_SMC |
0
|
5.345
|
3.7e-05
|
1.195
|
| HMC_vs_SMC |
1
|
4.933
|
9.24e-05
|
1.103
|
| HMC_vs_SMC |
2
|
4.875
|
0.000105
|
1.090
|
| HMC_vs_SMC |
3
|
3.826
|
0.00114
|
0.856
|
| HMC_vs_SMC |
4
|
4.074
|
0.000647
|
0.911
|
| HMC_vs_SMC |
5
|
6.318
|
4.6e-06
|
1.413
|
| Metro_vs_SMC |
0
|
4.421
|
0.000293
|
0.989
|
| Metro_vs_SMC |
1
|
6.577
|
2.7e-06
|
1.471
|
| Metro_vs_SMC |
2
|
6.198
|
5.91e-06
|
1.386
|
| Metro_vs_SMC |
3
|
4.259
|
0.000424
|
0.952
|
| Metro_vs_SMC |
4
|
4.104
|
0.000605
|
0.918
|
| Metro_vs_SMC |
5
|
6.390
|
3.96e-06
|
1.429
|
| HMC_vs_DEMetro_Z |
0
|
2.746
|
0.0128
|
0.614
|
| HMC_vs_DEMetro_Z |
1
|
1.256
|
0.224
|
0.281
|
| HMC_vs_DEMetro_Z |
2
|
1.698
|
0.106
|
0.380
|
| HMC_vs_DEMetro_Z |
3
|
1.090
|
0.289
|
0.244
|
| HMC_vs_DEMetro_Z |
4
|
0.110
|
0.914
|
0.025
|
| HMC_vs_DEMetro_Z |
5
|
0.228
|
0.822
|
0.051
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.053 |
0.015 |
0.007 |
5.484 |
| HMC |
8 |
0.212 |
0.012 |
0.006 |
35.557 |
| HMC |
10 |
0.213 |
0.011 |
0.007 |
27.802 |
| HMC |
12 |
0.229 |
0.014 |
0.010 |
21.237 |
| HMC |
15 |
0.186 |
0.010 |
0.006 |
29.920 |
| HMC |
18 |
0.317 |
0.012 |
0.008 |
38.047 |
| SMC |
5 |
0.013 |
0.015 |
0.007 |
-0.302 |
| SMC |
8 |
0.014 |
0.012 |
0.006 |
0.398 |
| SMC |
10 |
0.014 |
0.011 |
0.007 |
0.499 |
| SMC |
12 |
0.016 |
0.014 |
0.010 |
0.234 |
| SMC |
15 |
0.010 |
0.010 |
0.006 |
0.115 |
| SMC |
18 |
0.010 |
0.012 |
0.008 |
-0.273 |
| Metro |
5 |
0.032 |
0.015 |
0.007 |
2.518 |
| Metro |
8 |
0.127 |
0.012 |
0.006 |
20.476 |
| Metro |
10 |
0.243 |
0.011 |
0.007 |
31.862 |
| Metro |
12 |
0.250 |
0.014 |
0.010 |
23.307 |
| Metro |
15 |
0.185 |
0.010 |
0.006 |
29.673 |
| Metro |
18 |
0.338 |
0.012 |
0.008 |
40.626 |
| DEMetro_Z |
5 |
0.029 |
0.015 |
0.007 |
2.081 |
| DEMetro_Z |
8 |
0.144 |
0.012 |
0.006 |
23.426 |
| DEMetro_Z |
10 |
0.136 |
0.011 |
0.007 |
17.216 |
| DEMetro_Z |
12 |
0.163 |
0.014 |
0.010 |
14.798 |
| DEMetro_Z |
15 |
0.182 |
0.010 |
0.006 |
29.145 |
| DEMetro_Z |
18 |
0.305 |
0.012 |
0.008 |
36.630 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.179 |
0.000296 |
2.359 |
| HMC |
8 |
7.671 |
3.08e-07 |
60.191 |
| HMC |
10 |
205.835 |
5.26e-58 |
71.745 |
| HMC |
12 |
200.525 |
6.99e-58 |
58.922 |
| HMC |
15 |
220.540 |
5.41e-53 |
91.369 |
| HMC |
18 |
239.669 |
2.83e-57 |
66.098 |
| SMC |
5 |
-0.464 |
0.646 |
-0.156 |
| SMC |
8 |
1.193 |
0.24 |
0.416 |
| SMC |
10 |
0.656 |
0.516 |
0.200 |
| SMC |
12 |
-0.229 |
0.82 |
-0.062 |
| SMC |
15 |
1.250 |
0.22 |
0.496 |
| SMC |
18 |
-0.412 |
0.683 |
-0.118 |
| Metro |
5 |
3.764 |
0.000889 |
2.193 |
| Metro |
8 |
5.229 |
4.63e-05 |
16.633 |
| Metro |
10 |
5.898 |
1.09e-05 |
27.102 |
| Metro |
12 |
21.318 |
7.16e-15 |
55.143 |
| Metro |
15 |
206.644 |
5.07e-50 |
90.767 |
| Metro |
18 |
233.491 |
1.47e-58 |
66.074 |
| DEMetro_Z |
5 |
3.117 |
0.00431 |
1.644 |
| DEMetro_Z |
8 |
3.374 |
0.00313 |
7.758 |
| DEMetro_Z |
10 |
4.249 |
0.000433 |
30.353 |
| DEMetro_Z |
12 |
8.119 |
1.31e-07 |
44.906 |
| DEMetro_Z |
15 |
22.247 |
3.95e-15 |
88.233 |
| DEMetro_Z |
18 |
11.225 |
7.58e-10 |
56.832 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
0.999
|
0.331
|
0.223
|
| HMC_vs_DEMetro_Z |
1
|
6.847
|
1.56e-06
|
1.531
|
| HMC_vs_DEMetro_Z |
2
|
5.744
|
1.55e-05
|
1.284
|
| HMC_vs_DEMetro_Z |
3
|
2.516
|
0.021
|
0.563
|
| HMC_vs_DEMetro_Z |
4
|
0.791
|
0.439
|
0.177
|
| HMC_vs_DEMetro_Z |
5
|
1.823
|
0.084
|
0.408
|
| Metro_vs_SMC |
0
|
4.580
|
0.000205
|
1.024
|
| Metro_vs_SMC |
1
|
5.115
|
6.16e-05
|
1.144
|
| Metro_vs_SMC |
2
|
5.970
|
9.56e-06
|
1.335
|
| Metro_vs_SMC |
3
|
21.431
|
9.04e-15
|
4.792
|
| Metro_vs_SMC |
4
|
138.245
|
5.35e-30
|
30.913
|
| Metro_vs_SMC |
5
|
244.951
|
1.03e-34
|
54.773
|
| Metro_vs_DEMetro_Z |
0
|
0.750
|
0.462
|
0.168
|
| Metro_vs_DEMetro_Z |
1
|
2.012
|
0.0587
|
0.450
|
| Metro_vs_DEMetro_Z |
2
|
-0.340
|
0.738
|
-0.076
|
| Metro_vs_DEMetro_Z |
3
|
1.549
|
0.138
|
0.346
|
| Metro_vs_DEMetro_Z |
4
|
0.633
|
0.535
|
0.141
|
| Metro_vs_DEMetro_Z |
5
|
1.817
|
0.0851
|
0.406
|
| HMC_vs_Metro |
0
|
0.225
|
0.824
|
0.050
|
| HMC_vs_Metro |
1
|
5.421
|
3.13e-05
|
1.212
|
| HMC_vs_Metro |
2
|
9.637
|
9.51e-09
|
2.155
|
| HMC_vs_Metro |
3
|
1.465
|
0.159
|
0.327
|
| HMC_vs_Metro |
4
|
1.362
|
0.189
|
0.304
|
| HMC_vs_Metro |
5
|
0.484
|
0.634
|
0.108
|
| HMC_vs_SMC |
0
|
4.350
|
0.000345
|
0.973
|
| HMC_vs_SMC |
1
|
7.588
|
3.64e-07
|
1.697
|
| HMC_vs_SMC |
2
|
200.966
|
4.4e-33
|
44.937
|
| HMC_vs_SMC |
3
|
192.060
|
1.04e-32
|
42.946
|
| HMC_vs_SMC |
4
|
216.343
|
1.09e-33
|
48.376
|
| HMC_vs_SMC |
5
|
248.277
|
7.94e-35
|
55.516
|
| DEMetro_Z_vs_SMC |
0
|
3.021
|
0.00703
|
0.675
|
| DEMetro_Z_vs_SMC |
1
|
3.370
|
0.00322
|
0.754
|
| DEMetro_Z_vs_SMC |
2
|
4.251
|
0.000433
|
0.950
|
| DEMetro_Z_vs_SMC |
3
|
8.103
|
1.39e-07
|
1.812
|
| DEMetro_Z_vs_SMC |
4
|
22.575
|
3.49e-15
|
5.048
|
| DEMetro_Z_vs_SMC |
5
|
11.258
|
7.56e-10
|
2.517
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.120 |
0.045 |
0.032 |
2.359 |
| HMC |
8 |
1.840 |
0.051 |
0.030 |
60.191 |
| HMC |
10 |
3.539 |
0.054 |
0.049 |
71.745 |
| HMC |
12 |
4.229 |
0.089 |
0.070 |
58.922 |
| HMC |
15 |
5.298 |
0.086 |
0.057 |
91.369 |
| HMC |
18 |
6.358 |
0.128 |
0.094 |
66.098 |
| SMC |
5 |
0.040 |
0.045 |
0.032 |
-0.156 |
| SMC |
8 |
0.064 |
0.051 |
0.030 |
0.416 |
| SMC |
10 |
0.064 |
0.054 |
0.049 |
0.200 |
| SMC |
12 |
0.085 |
0.089 |
0.070 |
-0.062 |
| SMC |
15 |
0.114 |
0.086 |
0.057 |
0.496 |
| SMC |
18 |
0.117 |
0.128 |
0.094 |
-0.118 |
| Metro |
5 |
0.115 |
0.045 |
0.032 |
2.193 |
| Metro |
8 |
0.546 |
0.051 |
0.030 |
16.633 |
| Metro |
10 |
1.371 |
0.054 |
0.049 |
27.102 |
| Metro |
12 |
3.964 |
0.089 |
0.070 |
55.143 |
| Metro |
15 |
5.263 |
0.086 |
0.057 |
90.767 |
| Metro |
18 |
6.355 |
0.128 |
0.094 |
66.074 |
| DEMetro_Z |
5 |
0.097 |
0.045 |
0.032 |
1.644 |
| DEMetro_Z |
8 |
0.282 |
0.051 |
0.030 |
7.758 |
| DEMetro_Z |
10 |
1.529 |
0.054 |
0.049 |
30.353 |
| DEMetro_Z |
12 |
3.245 |
0.089 |
0.070 |
44.906 |
| DEMetro_Z |
15 |
5.119 |
0.086 |
0.057 |
88.233 |
| DEMetro_Z |
18 |
5.484 |
0.128 |
0.094 |
56.832 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.207 |
0.0337 |
0.781 |
| HMC |
8 |
5.394 |
3.32e-05 |
83.140 |
| HMC |
10 |
599.790 |
1.01e-73 |
216.356 |
| HMC |
12 |
628.482 |
2.01e-72 |
236.800 |
| HMC |
15 |
816.292 |
1.34e-66 |
372.523 |
| HMC |
18 |
1015.369 |
4.47e-77 |
401.194 |
| SMC |
5 |
1.538 |
0.132 |
0.510 |
| SMC |
8 |
0.545 |
0.589 |
0.196 |
| SMC |
10 |
-0.110 |
0.913 |
-0.033 |
| SMC |
12 |
0.227 |
0.822 |
0.071 |
| SMC |
15 |
-0.025 |
0.981 |
-0.010 |
| SMC |
18 |
-0.071 |
0.944 |
-0.025 |
| Metro |
5 |
3.220 |
0.00283 |
1.262 |
| Metro |
8 |
2.784 |
0.0117 |
8.468 |
| Metro |
10 |
3.679 |
0.00159 |
47.897 |
| Metro |
12 |
15.550 |
2.89e-12 |
216.312 |
| Metro |
15 |
773.758 |
1.47e-63 |
372.633 |
| Metro |
18 |
1062.125 |
3.02e-80 |
401.200 |
| DEMetro_Z |
5 |
3.802 |
0.000506 |
1.209 |
| DEMetro_Z |
8 |
2.827 |
0.0102 |
3.134 |
| DEMetro_Z |
10 |
3.435 |
0.00278 |
79.526 |
| DEMetro_Z |
12 |
7.711 |
2.88e-07 |
178.598 |
| DEMetro_Z |
15 |
19.031 |
7.8e-14 |
354.248 |
| DEMetro_Z |
18 |
10.453 |
2.56e-09 |
341.377 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.895
|
0.382
|
0.200
|
| HMC_vs_SMC |
1
|
5.363
|
3.56e-05
|
1.199
|
| HMC_vs_SMC |
2
|
568.725
|
1.15e-41
|
127.171
|
| HMC_vs_SMC |
3
|
626.417
|
1.84e-42
|
140.071
|
| HMC_vs_SMC |
4
|
787.495
|
2.38e-44
|
176.089
|
| HMC_vs_SMC |
5
|
1084.900
|
5.4e-47
|
242.591
|
| Metro_vs_DEMetro_Z |
0
|
0.143
|
0.887
|
0.032
|
| Metro_vs_DEMetro_Z |
1
|
1.545
|
0.139
|
0.346
|
| Metro_vs_DEMetro_Z |
2
|
-1.132
|
0.272
|
-0.253
|
| Metro_vs_DEMetro_Z |
3
|
1.294
|
0.211
|
0.289
|
| Metro_vs_DEMetro_Z |
4
|
0.987
|
0.336
|
0.221
|
| Metro_vs_DEMetro_Z |
5
|
1.833
|
0.0825
|
0.410
|
| HMC_vs_Metro |
0
|
-1.416
|
0.173
|
-0.317
|
| HMC_vs_Metro |
1
|
4.631
|
0.000182
|
1.035
|
| HMC_vs_Metro |
2
|
12.936
|
7.21e-11
|
2.893
|
| HMC_vs_Metro |
3
|
1.482
|
0.155
|
0.331
|
| HMC_vs_Metro |
4
|
-1.050
|
0.307
|
-0.235
|
| HMC_vs_Metro |
5
|
-0.105
|
0.917
|
-0.024
|
| HMC_vs_DEMetro_Z |
0
|
-1.188
|
0.25
|
-0.266
|
| HMC_vs_DEMetro_Z |
1
|
5.271
|
4.36e-05
|
1.179
|
| HMC_vs_DEMetro_Z |
2
|
5.907
|
1.09e-05
|
1.321
|
| HMC_vs_DEMetro_Z |
3
|
2.521
|
0.0208
|
0.564
|
| HMC_vs_DEMetro_Z |
4
|
0.977
|
0.341
|
0.219
|
| HMC_vs_DEMetro_Z |
5
|
1.834
|
0.0823
|
0.410
|
| Metro_vs_SMC |
0
|
1.867
|
0.0775
|
0.417
|
| Metro_vs_SMC |
1
|
2.842
|
0.0104
|
0.636
|
| Metro_vs_SMC |
2
|
3.662
|
0.00166
|
0.819
|
| Metro_vs_SMC |
3
|
15.494
|
3.11e-12
|
3.465
|
| Metro_vs_SMC |
4
|
760.805
|
4.58e-44
|
170.121
|
| Metro_vs_SMC |
5
|
1137.013
|
2.22e-47
|
254.244
|
| DEMetro_Z_vs_SMC |
0
|
1.882
|
0.0752
|
0.421
|
| DEMetro_Z_vs_SMC |
1
|
2.409
|
0.0263
|
0.539
|
| DEMetro_Z_vs_SMC |
2
|
3.435
|
0.00278
|
0.768
|
| DEMetro_Z_vs_SMC |
3
|
7.686
|
3.02e-07
|
1.719
|
| DEMetro_Z_vs_SMC |
4
|
19.022
|
7.9e-14
|
4.254
|
| DEMetro_Z_vs_SMC |
5
|
10.466
|
2.51e-09
|
2.340
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.087 |
0.048 |
0.050 |
0.781 |
| HMC |
8 |
6.151 |
0.081 |
0.073 |
83.140 |
| HMC |
10 |
17.659 |
0.119 |
0.081 |
216.356 |
| HMC |
12 |
25.471 |
0.161 |
0.107 |
236.800 |
| HMC |
15 |
39.766 |
0.204 |
0.106 |
372.523 |
| HMC |
18 |
57.267 |
0.197 |
0.142 |
401.194 |
| SMC |
5 |
0.074 |
0.048 |
0.050 |
0.510 |
| SMC |
8 |
0.095 |
0.081 |
0.073 |
0.196 |
| SMC |
10 |
0.116 |
0.119 |
0.081 |
-0.033 |
| SMC |
12 |
0.169 |
0.161 |
0.107 |
0.071 |
| SMC |
15 |
0.203 |
0.204 |
0.106 |
-0.010 |
| SMC |
18 |
0.193 |
0.197 |
0.142 |
-0.025 |
| Metro |
5 |
0.111 |
0.048 |
0.050 |
1.262 |
| Metro |
8 |
0.699 |
0.081 |
0.073 |
8.468 |
| Metro |
10 |
4.002 |
0.119 |
0.081 |
47.897 |
| Metro |
12 |
23.281 |
0.161 |
0.107 |
216.312 |
| Metro |
15 |
39.777 |
0.204 |
0.106 |
372.633 |
| Metro |
18 |
57.268 |
0.197 |
0.142 |
401.200 |
| DEMetro_Z |
5 |
0.108 |
0.048 |
0.050 |
1.209 |
| DEMetro_Z |
8 |
0.310 |
0.081 |
0.073 |
3.134 |
| DEMetro_Z |
10 |
6.566 |
0.119 |
0.081 |
79.526 |
| DEMetro_Z |
12 |
19.250 |
0.161 |
0.107 |
178.598 |
| DEMetro_Z |
15 |
37.825 |
0.204 |
0.106 |
354.248 |
| DEMetro_Z |
18 |
48.758 |
0.197 |
0.142 |
341.377 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.102 |
0.000403 |
2.628 |
| HMC |
8 |
7.510 |
4.21e-07 |
78.195 |
| HMC |
10 |
64.197 |
9.1e-25 |
84.322 |
| HMC |
12 |
66.483 |
5.23e-26 |
64.755 |
| HMC |
15 |
80.382 |
1.08e-26 |
106.958 |
| HMC |
18 |
71.315 |
9.82e-27 |
68.135 |
| SMC |
5 |
-0.664 |
0.511 |
-0.221 |
| SMC |
8 |
1.721 |
0.0945 |
0.691 |
| SMC |
10 |
0.404 |
0.689 |
0.123 |
| SMC |
12 |
-0.051 |
0.959 |
-0.014 |
| SMC |
15 |
1.423 |
0.164 |
0.585 |
| SMC |
18 |
-0.574 |
0.569 |
-0.163 |
| Metro |
5 |
3.754 |
0.000966 |
2.385 |
| Metro |
8 |
5.242 |
4.57e-05 |
22.249 |
| Metro |
10 |
5.744 |
1.53e-05 |
33.521 |
| Metro |
12 |
19.276 |
5.1e-14 |
61.645 |
| Metro |
15 |
77.906 |
2e-26 |
103.520 |
| Metro |
18 |
82.112 |
1.38e-28 |
70.729 |
| DEMetro_Z |
5 |
3.967 |
0.000536 |
2.362 |
| DEMetro_Z |
8 |
4.057 |
0.000654 |
10.186 |
| DEMetro_Z |
10 |
4.298 |
0.000387 |
36.570 |
| DEMetro_Z |
12 |
8.080 |
1.42e-07 |
50.027 |
| DEMetro_Z |
15 |
21.103 |
1.09e-14 |
103.330 |
| DEMetro_Z |
18 |
11.225 |
7.61e-10 |
58.789 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.028
|
0.978
|
0.006
|
| Metro_vs_DEMetro_Z |
1
|
2.210
|
0.0396
|
0.494
|
| Metro_vs_DEMetro_Z |
2
|
-0.264
|
0.795
|
-0.059
|
| Metro_vs_DEMetro_Z |
3
|
1.488
|
0.153
|
0.333
|
| Metro_vs_DEMetro_Z |
4
|
0.034
|
0.973
|
0.008
|
| Metro_vs_DEMetro_Z |
5
|
2.228
|
0.0381
|
0.498
|
| DEMetro_Z_vs_SMC |
0
|
3.886
|
0.000994
|
0.869
|
| DEMetro_Z_vs_SMC |
1
|
4.017
|
0.000737
|
0.898
|
| DEMetro_Z_vs_SMC |
2
|
4.302
|
0.000384
|
0.962
|
| DEMetro_Z_vs_SMC |
3
|
8.057
|
1.51e-07
|
1.802
|
| DEMetro_Z_vs_SMC |
4
|
21.214
|
1.09e-14
|
4.744
|
| DEMetro_Z_vs_SMC |
5
|
11.247
|
7.68e-10
|
2.515
|
| HMC_vs_DEMetro_Z |
0
|
0.316
|
0.755
|
0.071
|
| HMC_vs_DEMetro_Z |
1
|
6.678
|
2.19e-06
|
1.493
|
| HMC_vs_DEMetro_Z |
2
|
5.486
|
2.72e-05
|
1.227
|
| HMC_vs_DEMetro_Z |
3
|
2.383
|
0.0277
|
0.533
|
| HMC_vs_DEMetro_Z |
4
|
0.777
|
0.447
|
0.174
|
| HMC_vs_DEMetro_Z |
5
|
1.701
|
0.105
|
0.380
|
| HMC_vs_Metro |
0
|
0.291
|
0.774
|
0.065
|
| HMC_vs_Metro |
1
|
5.163
|
5.53e-05
|
1.155
|
| HMC_vs_Metro |
2
|
8.252
|
1.05e-07
|
1.845
|
| HMC_vs_Metro |
3
|
0.903
|
0.378
|
0.202
|
| HMC_vs_Metro |
4
|
1.569
|
0.133
|
0.351
|
| HMC_vs_Metro |
5
|
-2.044
|
0.0551
|
-0.457
|
| HMC_vs_SMC |
0
|
4.319
|
0.00037
|
0.966
|
| HMC_vs_SMC |
1
|
7.416
|
5.07e-07
|
1.658
|
| HMC_vs_SMC |
2
|
61.611
|
2.41e-23
|
13.777
|
| HMC_vs_SMC |
3
|
64.450
|
1.03e-23
|
14.411
|
| HMC_vs_SMC |
4
|
76.741
|
3.77e-25
|
17.160
|
| HMC_vs_SMC |
5
|
75.814
|
4.75e-25
|
16.952
|
| Metro_vs_SMC |
0
|
4.444
|
0.000279
|
0.994
|
| Metro_vs_SMC |
1
|
5.131
|
5.94e-05
|
1.147
|
| Metro_vs_SMC |
2
|
5.829
|
1.29e-05
|
1.303
|
| Metro_vs_SMC |
3
|
19.216
|
6.58e-14
|
4.297
|
| Metro_vs_SMC |
4
|
74.049
|
7.42e-25
|
16.558
|
| Metro_vs_SMC |
5
|
94.630
|
7.11e-27
|
21.160
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.119 |
0.057 |
0.024 |
2.628 |
| HMC |
8 |
1.635 |
0.060 |
0.020 |
78.195 |
| HMC |
10 |
3.094 |
0.068 |
0.036 |
84.322 |
| HMC |
12 |
3.850 |
0.097 |
0.058 |
64.755 |
| HMC |
15 |
4.821 |
0.090 |
0.044 |
106.958 |
| HMC |
18 |
5.602 |
0.132 |
0.080 |
68.135 |
| SMC |
5 |
0.051 |
0.057 |
0.024 |
-0.221 |
| SMC |
8 |
0.074 |
0.060 |
0.020 |
0.691 |
| SMC |
10 |
0.072 |
0.068 |
0.036 |
0.123 |
| SMC |
12 |
0.096 |
0.097 |
0.058 |
-0.014 |
| SMC |
15 |
0.116 |
0.090 |
0.044 |
0.585 |
| SMC |
18 |
0.119 |
0.132 |
0.080 |
-0.163 |
| Metro |
5 |
0.113 |
0.057 |
0.024 |
2.385 |
| Metro |
8 |
0.508 |
0.060 |
0.020 |
22.249 |
| Metro |
10 |
1.271 |
0.068 |
0.036 |
33.521 |
| Metro |
12 |
3.670 |
0.097 |
0.058 |
61.645 |
| Metro |
15 |
4.669 |
0.090 |
0.044 |
103.520 |
| Metro |
18 |
5.810 |
0.132 |
0.080 |
70.729 |
| DEMetro_Z |
5 |
0.113 |
0.057 |
0.024 |
2.362 |
| DEMetro_Z |
8 |
0.265 |
0.060 |
0.020 |
10.186 |
| DEMetro_Z |
10 |
1.381 |
0.068 |
0.036 |
36.570 |
| DEMetro_Z |
12 |
2.996 |
0.097 |
0.058 |
50.027 |
| DEMetro_Z |
15 |
4.660 |
0.090 |
0.044 |
103.330 |
| DEMetro_Z |
18 |
4.851 |
0.132 |
0.080 |
58.789 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.289 |
0.000275 |
3.101 |
| HMC |
8 |
7.599 |
3.54e-07 |
69.515 |
| HMC |
10 |
110.775 |
1.97e-32 |
83.728 |
| HMC |
12 |
142.487 |
7.86e-47 |
59.086 |
| HMC |
15 |
133.738 |
3.95e-34 |
102.683 |
| HMC |
18 |
137.170 |
4.05e-39 |
75.035 |
| SMC |
5 |
-0.242 |
0.81 |
-0.085 |
| SMC |
8 |
1.041 |
0.304 |
0.346 |
| SMC |
10 |
0.540 |
0.592 |
0.169 |
| SMC |
12 |
-0.506 |
0.616 |
-0.134 |
| SMC |
15 |
1.391 |
0.173 |
0.561 |
| SMC |
18 |
-0.412 |
0.683 |
-0.127 |
| Metro |
5 |
3.614 |
0.00143 |
2.492 |
| Metro |
8 |
5.139 |
5.7e-05 |
18.851 |
| Metro |
10 |
6.120 |
6.86e-06 |
32.124 |
| Metro |
12 |
22.310 |
2.99e-15 |
55.423 |
| Metro |
15 |
124.114 |
7.35e-33 |
101.576 |
| Metro |
18 |
145.920 |
5.38e-41 |
75.575 |
| DEMetro_Z |
5 |
3.524 |
0.0018 |
2.481 |
| DEMetro_Z |
8 |
3.542 |
0.00214 |
9.008 |
| DEMetro_Z |
10 |
4.318 |
0.00037 |
36.272 |
| DEMetro_Z |
12 |
8.210 |
1.11e-07 |
45.552 |
| DEMetro_Z |
15 |
22.216 |
4.17e-15 |
98.917 |
| DEMetro_Z |
18 |
11.334 |
6.53e-10 |
65.844 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
3.247
|
0.00424
|
0.726
|
| DEMetro_Z_vs_SMC |
1
|
3.537
|
0.0022
|
0.791
|
| DEMetro_Z_vs_SMC |
2
|
4.314
|
0.000375
|
0.965
|
| DEMetro_Z_vs_SMC |
3
|
8.204
|
1.15e-07
|
1.835
|
| DEMetro_Z_vs_SMC |
4
|
22.441
|
3.89e-15
|
5.018
|
| DEMetro_Z_vs_SMC |
5
|
11.329
|
6.8e-10
|
2.533
|
| HMC_vs_Metro |
0
|
0.665
|
0.514
|
0.149
|
| HMC_vs_Metro |
1
|
5.442
|
2.99e-05
|
1.217
|
| HMC_vs_Metro |
2
|
9.522
|
1.15e-08
|
2.129
|
| HMC_vs_Metro |
3
|
1.406
|
0.176
|
0.314
|
| HMC_vs_Metro |
4
|
1.487
|
0.153
|
0.333
|
| HMC_vs_Metro |
5
|
-0.946
|
0.356
|
-0.211
|
| Metro_vs_DEMetro_Z |
0
|
0.011
|
0.991
|
0.002
|
| Metro_vs_DEMetro_Z |
1
|
1.968
|
0.0638
|
0.440
|
| Metro_vs_DEMetro_Z |
2
|
-0.369
|
0.717
|
-0.082
|
| Metro_vs_DEMetro_Z |
3
|
1.489
|
0.153
|
0.333
|
| Metro_vs_DEMetro_Z |
4
|
0.539
|
0.596
|
0.120
|
| Metro_vs_DEMetro_Z |
5
|
1.636
|
0.118
|
0.366
|
| HMC_vs_SMC |
0
|
4.264
|
0.00042
|
0.953
|
| HMC_vs_SMC |
1
|
7.537
|
4.02e-07
|
1.685
|
| HMC_vs_SMC |
2
|
103.547
|
1.29e-27
|
23.154
|
| HMC_vs_SMC |
3
|
149.763
|
1.17e-30
|
33.488
|
| HMC_vs_SMC |
4
|
111.375
|
3.24e-28
|
24.904
|
| HMC_vs_SMC |
5
|
144.120
|
2.43e-30
|
32.226
|
| Metro_vs_SMC |
0
|
3.952
|
0.000856
|
0.884
|
| Metro_vs_SMC |
1
|
5.092
|
6.48e-05
|
1.139
|
| Metro_vs_SMC |
2
|
6.213
|
5.73e-06
|
1.389
|
| Metro_vs_SMC |
3
|
22.478
|
3.77e-15
|
5.026
|
| Metro_vs_SMC |
4
|
108.659
|
5.17e-28
|
24.297
|
| Metro_vs_SMC |
5
|
131.901
|
1.31e-29
|
29.494
|
| HMC_vs_DEMetro_Z |
0
|
0.623
|
0.541
|
0.139
|
| HMC_vs_DEMetro_Z |
1
|
6.711
|
2.05e-06
|
1.501
|
| HMC_vs_DEMetro_Z |
2
|
5.451
|
2.93e-05
|
1.219
|
| HMC_vs_DEMetro_Z |
3
|
2.424
|
0.0255
|
0.542
|
| HMC_vs_DEMetro_Z |
4
|
0.795
|
0.436
|
0.178
|
| HMC_vs_DEMetro_Z |
5
|
1.552
|
0.137
|
0.347
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.037 |
0.015 |
0.007 |
3.101 |
| HMC |
8 |
0.402 |
0.012 |
0.006 |
69.515 |
| HMC |
10 |
0.621 |
0.011 |
0.007 |
83.728 |
| HMC |
12 |
0.611 |
0.014 |
0.010 |
59.086 |
| HMC |
15 |
0.616 |
0.010 |
0.006 |
102.683 |
| HMC |
18 |
0.613 |
0.012 |
0.008 |
75.035 |
| SMC |
5 |
0.014 |
0.015 |
0.007 |
-0.085 |
| SMC |
8 |
0.014 |
0.012 |
0.006 |
0.346 |
| SMC |
10 |
0.012 |
0.011 |
0.007 |
0.169 |
| SMC |
12 |
0.013 |
0.014 |
0.010 |
-0.134 |
| SMC |
15 |
0.013 |
0.010 |
0.006 |
0.561 |
| SMC |
18 |
0.011 |
0.012 |
0.008 |
-0.127 |
| Metro |
5 |
0.032 |
0.015 |
0.007 |
2.492 |
| Metro |
8 |
0.118 |
0.012 |
0.006 |
18.851 |
| Metro |
10 |
0.245 |
0.011 |
0.007 |
32.124 |
| Metro |
12 |
0.574 |
0.014 |
0.010 |
55.423 |
| Metro |
15 |
0.609 |
0.010 |
0.006 |
101.576 |
| Metro |
18 |
0.618 |
0.012 |
0.008 |
75.575 |
| DEMetro_Z |
5 |
0.032 |
0.015 |
0.007 |
2.481 |
| DEMetro_Z |
8 |
0.063 |
0.012 |
0.006 |
9.008 |
| DEMetro_Z |
10 |
0.275 |
0.011 |
0.007 |
36.272 |
| DEMetro_Z |
12 |
0.474 |
0.014 |
0.010 |
45.552 |
| DEMetro_Z |
15 |
0.594 |
0.010 |
0.006 |
98.917 |
| DEMetro_Z |
18 |
0.540 |
0.012 |
0.008 |
65.844 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Dimension
(Mixture,
mm,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
1.912 |
0.0703 |
2.755 |
| HMC |
8 |
6.458 |
3.39e-06 |
34.732 |
| HMC |
10 |
4.713 |
0.00015 |
28.317 |
| HMC |
12 |
5.449 |
2.93e-05 |
39.830 |
| HMC |
15 |
6.260 |
5.17e-06 |
61.815 |
| HMC |
18 |
4.563 |
0.000212 |
35.542 |
| SMC |
5 |
0.265 |
0.793 |
0.143 |
| SMC |
8 |
0.464 |
0.645 |
0.138 |
| SMC |
10 |
0.578 |
0.567 |
0.179 |
| SMC |
12 |
-0.757 |
0.454 |
-0.207 |
| SMC |
15 |
1.537 |
0.134 |
0.641 |
| SMC |
18 |
1.413 |
0.166 |
0.474 |
| Metro |
5 |
10.570 |
5.26e-10 |
9.269 |
| Metro |
8 |
5.424 |
2.96e-05 |
13.980 |
| Metro |
10 |
5.119 |
6.05e-05 |
29.470 |
| Metro |
12 |
5.732 |
1.58e-05 |
36.701 |
| Metro |
15 |
6.414 |
3.75e-06 |
62.426 |
| Metro |
18 |
4.673 |
0.000165 |
35.916 |
| DEMetro_Z |
5 |
43.088 |
2.05e-20 |
2583.040 |
| DEMetro_Z |
8 |
30.152 |
1.64e-17 |
826.679 |
| DEMetro_Z |
10 |
42.608 |
2.51e-20 |
831.650 |
| DEMetro_Z |
12 |
40.636 |
6.08e-20 |
591.030 |
| DEMetro_Z |
15 |
29.417 |
2.59e-17 |
687.442 |
| DEMetro_Z |
18 |
26.811 |
1.44e-16 |
380.403 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-43.079
|
2.06e-20
|
-9.633
|
| HMC_vs_DEMetro_Z |
1
|
-27.539
|
8.88e-17
|
-6.158
|
| HMC_vs_DEMetro_Z |
2
|
-38.919
|
1.39e-19
|
-8.703
|
| HMC_vs_DEMetro_Z |
3
|
-37.789
|
2.42e-19
|
-8.450
|
| HMC_vs_DEMetro_Z |
4
|
-28.291
|
5.39e-17
|
-6.326
|
| HMC_vs_DEMetro_Z |
5
|
-24.844
|
5.98e-16
|
-5.555
|
| Metro_vs_SMC |
0
|
8.225
|
1.11e-07
|
1.839
|
| Metro_vs_SMC |
1
|
5.306
|
4.03e-05
|
1.186
|
| Metro_vs_SMC |
2
|
5.077
|
6.69e-05
|
1.135
|
| Metro_vs_SMC |
3
|
5.786
|
1.42e-05
|
1.294
|
| Metro_vs_SMC |
4
|
6.337
|
4.42e-06
|
1.417
|
| Metro_vs_SMC |
5
|
4.657
|
0.000172
|
1.041
|
| Metro_vs_DEMetro_Z |
0
|
-42.896
|
2.23e-20
|
-9.592
|
| Metro_vs_DEMetro_Z |
1
|
-30.415
|
1.4e-17
|
-6.801
|
| Metro_vs_DEMetro_Z |
2
|
-38.853
|
1.43e-19
|
-8.688
|
| Metro_vs_DEMetro_Z |
3
|
-33.498
|
2.31e-18
|
-7.490
|
| Metro_vs_DEMetro_Z |
4
|
-28.312
|
5.31e-17
|
-6.331
|
| Metro_vs_DEMetro_Z |
5
|
-24.867
|
5.88e-16
|
-5.561
|
| HMC_vs_Metro |
0
|
-4.854
|
0.00011
|
-1.085
|
| HMC_vs_Metro |
1
|
3.169
|
0.00505
|
0.709
|
| HMC_vs_Metro |
2
|
-0.162
|
0.873
|
-0.036
|
| HMC_vs_Metro |
3
|
0.773
|
0.449
|
0.173
|
| HMC_vs_Metro |
4
|
-2.946
|
0.00829
|
-0.659
|
| HMC_vs_Metro |
5
|
-2.522
|
0.0208
|
-0.564
|
| HMC_vs_SMC |
0
|
1.753
|
0.0957
|
0.392
|
| HMC_vs_SMC |
1
|
6.507
|
3.11e-06
|
1.455
|
| HMC_vs_SMC |
2
|
4.669
|
0.000167
|
1.044
|
| HMC_vs_SMC |
3
|
5.487
|
2.71e-05
|
1.227
|
| HMC_vs_SMC |
4
|
6.184
|
6.09e-06
|
1.383
|
| HMC_vs_SMC |
5
|
4.546
|
0.000221
|
1.016
|
| DEMetro_Z_vs_SMC |
0
|
43.025
|
2.11e-20
|
9.621
|
| DEMetro_Z_vs_SMC |
1
|
30.059
|
1.74e-17
|
6.721
|
| DEMetro_Z_vs_SMC |
2
|
42.802
|
2.33e-20
|
9.571
|
| DEMetro_Z_vs_SMC |
3
|
40.510
|
6.55e-20
|
9.058
|
| DEMetro_Z_vs_SMC |
4
|
29.293
|
2.82e-17
|
6.550
|
| DEMetro_Z_vs_SMC |
5
|
26.800
|
1.47e-16
|
5.993
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.031 |
0.024 |
0.003 |
2.755 |
| HMC |
8 |
0.313 |
0.028 |
0.008 |
34.732 |
| HMC |
10 |
0.260 |
0.029 |
0.008 |
28.317 |
| HMC |
12 |
0.468 |
0.033 |
0.011 |
39.830 |
| HMC |
15 |
0.629 |
0.032 |
0.010 |
61.815 |
| HMC |
18 |
0.678 |
0.038 |
0.018 |
35.542 |
| SMC |
5 |
0.024 |
0.024 |
0.003 |
0.143 |
| SMC |
8 |
0.030 |
0.028 |
0.008 |
0.138 |
| SMC |
10 |
0.031 |
0.029 |
0.008 |
0.179 |
| SMC |
12 |
0.031 |
0.033 |
0.011 |
-0.207 |
| SMC |
15 |
0.038 |
0.032 |
0.010 |
0.641 |
| SMC |
18 |
0.046 |
0.038 |
0.018 |
0.474 |
| Metro |
5 |
0.048 |
0.024 |
0.003 |
9.269 |
| Metro |
8 |
0.143 |
0.028 |
0.008 |
13.980 |
| Metro |
10 |
0.270 |
0.029 |
0.008 |
29.470 |
| Metro |
12 |
0.434 |
0.033 |
0.011 |
36.701 |
| Metro |
15 |
0.635 |
0.032 |
0.010 |
62.426 |
| Metro |
18 |
0.685 |
0.038 |
0.018 |
35.916 |
| DEMetro_Z |
5 |
6.848 |
0.024 |
0.003 |
2583.040 |
| DEMetro_Z |
8 |
6.807 |
0.028 |
0.008 |
826.679 |
| DEMetro_Z |
10 |
6.811 |
0.029 |
0.008 |
831.650 |
| DEMetro_Z |
12 |
6.476 |
0.033 |
0.011 |
591.030 |
| DEMetro_Z |
15 |
6.671 |
0.032 |
0.010 |
687.442 |
| DEMetro_Z |
18 |
6.893 |
0.038 |
0.018 |
380.403 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.883 |
0.00701 |
0.760 |
| HMC |
8 |
4.407 |
0.000302 |
34.003 |
| HMC |
10 |
4.914 |
9.58e-05 |
32.566 |
| HMC |
12 |
3.859 |
0.00106 |
75.287 |
| HMC |
15 |
4.178 |
0.000511 |
114.299 |
| HMC |
18 |
3.544 |
0.00217 |
164.615 |
| SMC |
5 |
2.045 |
0.0486 |
0.559 |
| SMC |
8 |
0.997 |
0.325 |
0.290 |
| SMC |
10 |
1.897 |
0.0676 |
0.874 |
| SMC |
12 |
1.176 |
0.248 |
0.497 |
| SMC |
15 |
2.244 |
0.0322 |
0.989 |
| SMC |
18 |
1.890 |
0.0692 |
0.952 |
| Metro |
5 |
6.034 |
6.58e-07 |
2.225 |
| Metro |
8 |
3.384 |
0.00303 |
6.593 |
| Metro |
10 |
2.762 |
0.0124 |
30.800 |
| Metro |
12 |
3.746 |
0.00137 |
63.048 |
| Metro |
15 |
4.226 |
0.000458 |
115.193 |
| Metro |
18 |
3.561 |
0.00208 |
165.106 |
| DEMetro_Z |
5 |
28.858 |
3.73e-17 |
17962.934 |
| DEMetro_Z |
8 |
26.601 |
1.69e-16 |
8041.650 |
| DEMetro_Z |
10 |
32.474 |
4.13e-18 |
8995.026 |
| DEMetro_Z |
12 |
28.583 |
4.45e-17 |
6617.466 |
| DEMetro_Z |
15 |
30.542 |
1.3e-17 |
6171.854 |
| DEMetro_Z |
18 |
27.356 |
1.01e-16 |
6883.164 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.859
|
0.401
|
0.192
|
| HMC_vs_SMC |
1
|
4.389
|
0.000316
|
0.981
|
| HMC_vs_SMC |
2
|
4.748
|
0.00014
|
1.062
|
| HMC_vs_SMC |
3
|
3.858
|
0.00106
|
0.863
|
| HMC_vs_SMC |
4
|
4.116
|
0.000588
|
0.920
|
| HMC_vs_SMC |
5
|
3.523
|
0.00227
|
0.788
|
| Metro_vs_DEMetro_Z |
0
|
-28.855
|
3.73e-17
|
-6.452
|
| Metro_vs_DEMetro_Z |
1
|
-26.586
|
1.71e-16
|
-5.945
|
| Metro_vs_DEMetro_Z |
2
|
-32.387
|
4.34e-18
|
-7.242
|
| Metro_vs_DEMetro_Z |
3
|
-28.419
|
4.96e-17
|
-6.355
|
| Metro_vs_DEMetro_Z |
4
|
-30.140
|
1.66e-17
|
-6.740
|
| Metro_vs_DEMetro_Z |
5
|
-24.953
|
5.51e-16
|
-5.580
|
| HMC_vs_Metro |
0
|
-4.416
|
0.000297
|
-0.988
|
| HMC_vs_Metro |
1
|
3.272
|
0.00401
|
0.732
|
| HMC_vs_Metro |
2
|
0.155
|
0.878
|
0.035
|
| HMC_vs_Metro |
3
|
1.131
|
0.272
|
0.253
|
| HMC_vs_Metro |
4
|
-1.636
|
0.118
|
-0.366
|
| HMC_vs_Metro |
5
|
-0.632
|
0.535
|
-0.141
|
| HMC_vs_DEMetro_Z |
0
|
-28.854
|
3.74e-17
|
-6.452
|
| HMC_vs_DEMetro_Z |
1
|
-26.269
|
2.13e-16
|
-5.874
|
| HMC_vs_DEMetro_Z |
2
|
-32.665
|
3.7e-18
|
-7.304
|
| HMC_vs_DEMetro_Z |
3
|
-29.080
|
3.23e-17
|
-6.502
|
| HMC_vs_DEMetro_Z |
4
|
-30.137
|
1.66e-17
|
-6.739
|
| HMC_vs_DEMetro_Z |
5
|
-24.952
|
5.52e-16
|
-5.579
|
| Metro_vs_SMC |
0
|
4.831
|
0.000116
|
1.080
|
| Metro_vs_SMC |
1
|
3.148
|
0.0053
|
0.704
|
| Metro_vs_SMC |
2
|
2.670
|
0.0151
|
0.597
|
| Metro_vs_SMC |
3
|
3.755
|
0.00134
|
0.840
|
| Metro_vs_SMC |
4
|
4.163
|
0.000528
|
0.931
|
| Metro_vs_SMC |
5
|
3.541
|
0.00218
|
0.792
|
| DEMetro_Z_vs_SMC |
0
|
28.858
|
3.73e-17
|
6.453
|
| DEMetro_Z_vs_SMC |
1
|
26.597
|
1.69e-16
|
5.947
|
| DEMetro_Z_vs_SMC |
2
|
32.468
|
4.14e-18
|
7.260
|
| DEMetro_Z_vs_SMC |
3
|
28.579
|
4.47e-17
|
6.390
|
| DEMetro_Z_vs_SMC |
4
|
30.549
|
1.29e-17
|
6.831
|
| DEMetro_Z_vs_SMC |
5
|
27.359
|
1e-16
|
6.118
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.046 |
0.039 |
0.009 |
0.760 |
| HMC |
8 |
0.746 |
0.048 |
0.021 |
34.003 |
| HMC |
10 |
0.653 |
0.049 |
0.019 |
32.566 |
| HMC |
12 |
1.903 |
0.053 |
0.025 |
75.287 |
| HMC |
15 |
3.105 |
0.053 |
0.027 |
114.299 |
| HMC |
18 |
4.456 |
0.057 |
0.027 |
164.615 |
| SMC |
5 |
0.044 |
0.039 |
0.009 |
0.559 |
| SMC |
8 |
0.054 |
0.048 |
0.021 |
0.290 |
| SMC |
10 |
0.065 |
0.049 |
0.019 |
0.874 |
| SMC |
12 |
0.066 |
0.053 |
0.025 |
0.497 |
| SMC |
15 |
0.079 |
0.053 |
0.027 |
0.989 |
| SMC |
18 |
0.083 |
0.057 |
0.027 |
0.952 |
| Metro |
5 |
0.059 |
0.039 |
0.009 |
2.225 |
| Metro |
8 |
0.183 |
0.048 |
0.021 |
6.593 |
| Metro |
10 |
0.620 |
0.049 |
0.019 |
30.800 |
| Metro |
12 |
1.602 |
0.053 |
0.025 |
63.048 |
| Metro |
15 |
3.129 |
0.053 |
0.027 |
115.193 |
| Metro |
18 |
4.469 |
0.057 |
0.027 |
165.106 |
| DEMetro_Z |
5 |
167.859 |
0.039 |
0.009 |
17962.934 |
| DEMetro_Z |
8 |
165.208 |
0.048 |
0.021 |
8041.650 |
| DEMetro_Z |
10 |
166.831 |
0.049 |
0.019 |
8995.026 |
| DEMetro_Z |
12 |
162.632 |
0.053 |
0.025 |
6617.466 |
| DEMetro_Z |
15 |
164.867 |
0.053 |
0.027 |
6171.854 |
| DEMetro_Z |
18 |
183.980 |
0.057 |
0.027 |
6883.164 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.073 |
0.0514 |
3.280 |
| HMC |
8 |
6.459 |
3.4e-06 |
45.670 |
| HMC |
10 |
4.765 |
0.000134 |
35.161 |
| HMC |
12 |
5.536 |
2.43e-05 |
48.249 |
| HMC |
15 |
6.315 |
4.62e-06 |
75.208 |
| HMC |
18 |
4.564 |
0.000212 |
41.610 |
| SMC |
5 |
0.838 |
0.408 |
0.359 |
| SMC |
8 |
0.957 |
0.345 |
0.298 |
| SMC |
10 |
0.862 |
0.394 |
0.262 |
| SMC |
12 |
-0.297 |
0.768 |
-0.082 |
| SMC |
15 |
1.850 |
0.0735 |
0.777 |
| SMC |
18 |
1.707 |
0.096 |
0.561 |
| Metro |
5 |
11.051 |
2.36e-10 |
9.752 |
| Metro |
8 |
5.141 |
5.67e-05 |
18.227 |
| Metro |
10 |
4.953 |
8.79e-05 |
37.134 |
| Metro |
12 |
5.881 |
1.15e-05 |
45.556 |
| Metro |
15 |
6.458 |
3.43e-06 |
78.153 |
| Metro |
18 |
4.714 |
0.000151 |
43.349 |
| DEMetro_Z |
5 |
53.747 |
3.18e-22 |
5686.603 |
| DEMetro_Z |
8 |
44.030 |
1.36e-20 |
2027.008 |
| DEMetro_Z |
10 |
74.010 |
7.45e-25 |
1983.290 |
| DEMetro_Z |
12 |
46.966 |
4.03e-21 |
1358.676 |
| DEMetro_Z |
15 |
58.811 |
5.77e-23 |
1596.548 |
| DEMetro_Z |
18 |
55.965 |
1.46e-22 |
856.754 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-53.459
|
3.52e-22
|
-11.954
|
| Metro_vs_DEMetro_Z |
1
|
-43.789
|
1.51e-20
|
-9.791
|
| Metro_vs_DEMetro_Z |
2
|
-72.270
|
1.18e-24
|
-16.160
|
| Metro_vs_DEMetro_Z |
3
|
-43.913
|
1.44e-20
|
-9.819
|
| Metro_vs_DEMetro_Z |
4
|
-55.627
|
1.66e-22
|
-12.439
|
| Metro_vs_DEMetro_Z |
5
|
-44.968
|
9.18e-21
|
-10.055
|
| DEMetro_Z_vs_SMC |
0
|
53.758
|
3.17e-22
|
12.021
|
| DEMetro_Z_vs_SMC |
1
|
43.950
|
1.41e-20
|
9.828
|
| DEMetro_Z_vs_SMC |
2
|
74.130
|
7.27e-25
|
16.576
|
| DEMetro_Z_vs_SMC |
3
|
46.927
|
4.11e-21
|
10.493
|
| DEMetro_Z_vs_SMC |
4
|
58.658
|
6.1e-23
|
13.116
|
| DEMetro_Z_vs_SMC |
5
|
55.923
|
1.5e-22
|
12.505
|
| HMC_vs_DEMetro_Z |
0
|
-53.664
|
3.27e-22
|
-12.000
|
| HMC_vs_DEMetro_Z |
1
|
-40.771
|
5.8e-20
|
-9.117
|
| HMC_vs_DEMetro_Z |
2
|
-80.321
|
1.59e-25
|
-17.960
|
| HMC_vs_DEMetro_Z |
3
|
-46.575
|
4.74e-21
|
-10.414
|
| HMC_vs_DEMetro_Z |
4
|
-54.952
|
2.09e-22
|
-12.288
|
| HMC_vs_DEMetro_Z |
5
|
-45.218
|
8.27e-21
|
-10.111
|
| HMC_vs_Metro |
0
|
-4.171
|
0.000518
|
-0.933
|
| HMC_vs_Metro |
1
|
3.141
|
0.00538
|
0.702
|
| HMC_vs_Metro |
2
|
-0.216
|
0.831
|
-0.048
|
| HMC_vs_Metro |
3
|
0.567
|
0.577
|
0.127
|
| HMC_vs_Metro |
4
|
-2.494
|
0.022
|
-0.558
|
| HMC_vs_Metro |
5
|
-2.010
|
0.0589
|
-0.449
|
| HMC_vs_SMC |
0
|
1.825
|
0.0837
|
0.408
|
| HMC_vs_SMC |
1
|
6.484
|
3.26e-06
|
1.450
|
| HMC_vs_SMC |
2
|
4.701
|
0.000156
|
1.051
|
| HMC_vs_SMC |
3
|
5.557
|
2.33e-05
|
1.243
|
| HMC_vs_SMC |
4
|
6.238
|
5.44e-06
|
1.395
|
| HMC_vs_SMC |
5
|
4.542
|
0.000223
|
1.016
|
| Metro_vs_SMC |
0
|
9.002
|
2.78e-08
|
2.013
|
| Metro_vs_SMC |
1
|
4.971
|
8.48e-05
|
1.112
|
| Metro_vs_SMC |
2
|
4.909
|
9.75e-05
|
1.098
|
| Metro_vs_SMC |
3
|
5.914
|
1.08e-05
|
1.322
|
| Metro_vs_SMC |
4
|
6.385
|
4e-06
|
1.428
|
| Metro_vs_SMC |
5
|
4.694
|
0.000158
|
1.050
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.037 |
0.031 |
0.002 |
3.280 |
| HMC |
8 |
0.258 |
0.035 |
0.005 |
45.670 |
| HMC |
10 |
0.214 |
0.036 |
0.005 |
35.161 |
| HMC |
12 |
0.381 |
0.040 |
0.007 |
48.249 |
| HMC |
15 |
0.503 |
0.040 |
0.006 |
75.208 |
| HMC |
18 |
0.544 |
0.044 |
0.012 |
41.610 |
| SMC |
5 |
0.032 |
0.031 |
0.002 |
0.359 |
| SMC |
8 |
0.036 |
0.035 |
0.005 |
0.298 |
| SMC |
10 |
0.038 |
0.036 |
0.005 |
0.262 |
| SMC |
12 |
0.039 |
0.040 |
0.007 |
-0.082 |
| SMC |
15 |
0.045 |
0.040 |
0.006 |
0.777 |
| SMC |
18 |
0.051 |
0.044 |
0.012 |
0.561 |
| Metro |
5 |
0.048 |
0.031 |
0.002 |
9.752 |
| Metro |
8 |
0.124 |
0.035 |
0.005 |
18.227 |
| Metro |
10 |
0.224 |
0.036 |
0.005 |
37.134 |
| Metro |
12 |
0.362 |
0.040 |
0.007 |
45.556 |
| Metro |
15 |
0.522 |
0.040 |
0.006 |
78.153 |
| Metro |
18 |
0.565 |
0.044 |
0.012 |
43.349 |
| DEMetro_Z |
5 |
10.112 |
0.031 |
0.002 |
5686.603 |
| DEMetro_Z |
8 |
9.938 |
0.035 |
0.005 |
2027.008 |
| DEMetro_Z |
10 |
10.068 |
0.036 |
0.005 |
1983.290 |
| DEMetro_Z |
12 |
9.665 |
0.040 |
0.007 |
1358.676 |
| DEMetro_Z |
15 |
9.881 |
0.040 |
0.006 |
1596.548 |
| DEMetro_Z |
18 |
10.340 |
0.044 |
0.012 |
856.754 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.429 |
0.0246 |
3.167 |
| HMC |
8 |
6.338 |
4.37e-06 |
43.513 |
| HMC |
10 |
4.740 |
0.000142 |
31.864 |
| HMC |
12 |
5.419 |
3.13e-05 |
47.476 |
| HMC |
15 |
6.349 |
4.3e-06 |
71.149 |
| HMC |
18 |
4.584 |
0.000202 |
43.579 |
| SMC |
5 |
1.615 |
0.117 |
0.734 |
| SMC |
8 |
0.957 |
0.344 |
0.291 |
| SMC |
10 |
1.020 |
0.314 |
0.311 |
| SMC |
12 |
-0.454 |
0.652 |
-0.129 |
| SMC |
15 |
1.739 |
0.0917 |
0.738 |
| SMC |
18 |
1.088 |
0.284 |
0.364 |
| Metro |
5 |
11.304 |
1.26e-10 |
9.345 |
| Metro |
8 |
5.412 |
3.09e-05 |
17.373 |
| Metro |
10 |
4.886 |
0.000102 |
33.136 |
| Metro |
12 |
5.602 |
2.1e-05 |
43.412 |
| Metro |
15 |
6.427 |
3.66e-06 |
71.909 |
| Metro |
18 |
4.668 |
0.000167 |
44.296 |
| DEMetro_Z |
5 |
118.922 |
6.21e-29 |
433.276 |
| DEMetro_Z |
8 |
64.121 |
6.99e-24 |
189.913 |
| DEMetro_Z |
10 |
60.526 |
2.15e-23 |
183.237 |
| DEMetro_Z |
12 |
81.094 |
3.14e-26 |
146.717 |
| DEMetro_Z |
15 |
68.599 |
1.68e-24 |
180.149 |
| DEMetro_Z |
18 |
95.045 |
1.98e-28 |
114.669 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
114.987
|
1.77e-28
|
25.712
|
| DEMetro_Z_vs_SMC |
1
|
64.510
|
1.01e-23
|
14.425
|
| DEMetro_Z_vs_SMC |
2
|
60.131
|
3.82e-23
|
13.446
|
| DEMetro_Z_vs_SMC |
3
|
79.581
|
1.9e-25
|
17.795
|
| DEMetro_Z_vs_SMC |
4
|
65.247
|
8.15e-24
|
14.590
|
| DEMetro_Z_vs_SMC |
5
|
97.363
|
4.15e-27
|
21.771
|
| HMC_vs_Metro |
0
|
-4.541
|
0.000224
|
-1.015
|
| HMC_vs_Metro |
1
|
3.147
|
0.00531
|
0.704
|
| HMC_vs_Metro |
2
|
-0.154
|
0.879
|
-0.035
|
| HMC_vs_Metro |
3
|
0.852
|
0.405
|
0.191
|
| HMC_vs_Metro |
4
|
-1.115
|
0.279
|
-0.249
|
| HMC_vs_Metro |
5
|
-1.697
|
0.106
|
-0.380
|
| Metro_vs_DEMetro_Z |
0
|
-112.302
|
2.77e-28
|
-25.112
|
| Metro_vs_DEMetro_Z |
1
|
-45.527
|
7.28e-21
|
-10.180
|
| Metro_vs_DEMetro_Z |
2
|
-18.468
|
1.35e-13
|
-4.130
|
| Metro_vs_DEMetro_Z |
3
|
-12.660
|
1.04e-10
|
-2.831
|
| Metro_vs_DEMetro_Z |
4
|
-9.645
|
9.39e-09
|
-2.157
|
| Metro_vs_DEMetro_Z |
5
|
-7.565
|
3.8e-07
|
-1.692
|
| HMC_vs_SMC |
0
|
1.876
|
0.0762
|
0.419
|
| HMC_vs_SMC |
1
|
6.333
|
4.46e-06
|
1.416
|
| HMC_vs_SMC |
2
|
4.675
|
0.000165
|
1.045
|
| HMC_vs_SMC |
3
|
5.452
|
2.93e-05
|
1.219
|
| HMC_vs_SMC |
4
|
6.270
|
5.09e-06
|
1.402
|
| HMC_vs_SMC |
5
|
4.573
|
0.000208
|
1.023
|
| Metro_vs_SMC |
0
|
8.966
|
2.96e-08
|
2.005
|
| Metro_vs_SMC |
1
|
5.249
|
4.57e-05
|
1.174
|
| Metro_vs_SMC |
2
|
4.830
|
0.000116
|
1.080
|
| Metro_vs_SMC |
3
|
5.649
|
1.91e-05
|
1.263
|
| Metro_vs_SMC |
4
|
6.345
|
4.35e-06
|
1.419
|
| Metro_vs_SMC |
5
|
4.658
|
0.000172
|
1.041
|
| HMC_vs_DEMetro_Z |
0
|
-107.477
|
6.36e-28
|
-24.033
|
| HMC_vs_DEMetro_Z |
1
|
-17.258
|
4.56e-13
|
-3.859
|
| HMC_vs_DEMetro_Z |
2
|
-17.307
|
4.34e-13
|
-3.870
|
| HMC_vs_DEMetro_Z |
3
|
-11.047
|
1.03e-09
|
-2.470
|
| HMC_vs_DEMetro_Z |
4
|
-9.660
|
9.17e-09
|
-2.160
|
| HMC_vs_DEMetro_Z |
5
|
-7.615
|
3.46e-07
|
-1.703
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.018 |
0.013 |
0.001 |
3.167 |
| HMC |
8 |
0.144 |
0.014 |
0.003 |
43.513 |
| HMC |
10 |
0.113 |
0.014 |
0.003 |
31.864 |
| HMC |
12 |
0.194 |
0.015 |
0.004 |
47.476 |
| HMC |
15 |
0.231 |
0.012 |
0.003 |
71.149 |
| HMC |
18 |
0.225 |
0.013 |
0.005 |
43.579 |
| SMC |
5 |
0.014 |
0.013 |
0.001 |
0.734 |
| SMC |
8 |
0.015 |
0.014 |
0.003 |
0.291 |
| SMC |
10 |
0.015 |
0.014 |
0.003 |
0.311 |
| SMC |
12 |
0.014 |
0.015 |
0.004 |
-0.129 |
| SMC |
15 |
0.015 |
0.012 |
0.003 |
0.738 |
| SMC |
18 |
0.015 |
0.013 |
0.005 |
0.364 |
| Metro |
5 |
0.026 |
0.013 |
0.001 |
9.345 |
| Metro |
8 |
0.066 |
0.014 |
0.003 |
17.373 |
| Metro |
10 |
0.117 |
0.014 |
0.003 |
33.136 |
| Metro |
12 |
0.179 |
0.015 |
0.004 |
43.412 |
| Metro |
15 |
0.233 |
0.012 |
0.003 |
71.909 |
| Metro |
18 |
0.229 |
0.013 |
0.005 |
44.296 |
| DEMetro_Z |
5 |
0.577 |
0.013 |
0.001 |
433.276 |
| DEMetro_Z |
8 |
0.580 |
0.014 |
0.003 |
189.913 |
| DEMetro_Z |
10 |
0.581 |
0.014 |
0.003 |
183.237 |
| DEMetro_Z |
12 |
0.569 |
0.015 |
0.004 |
146.717 |
| DEMetro_Z |
15 |
0.566 |
0.012 |
0.003 |
180.149 |
| DEMetro_Z |
18 |
0.572 |
0.013 |
0.005 |
114.669 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.505 |
0.0204 |
2.294 |
| HMC |
8 |
7.741 |
2.69e-07 |
54.973 |
| HMC |
10 |
277.932 |
2.78e-58 |
109.440 |
| HMC |
12 |
280.798 |
6.31e-63 |
98.020 |
| HMC |
15 |
225.336 |
2.35e-42 |
138.777 |
| HMC |
18 |
202.264 |
9.06e-50 |
88.752 |
| SMC |
5 |
1.247 |
0.221 |
0.497 |
| SMC |
8 |
-1.558 |
0.128 |
-0.450 |
| SMC |
10 |
0.833 |
0.41 |
0.282 |
| SMC |
12 |
-1.866 |
0.0699 |
-0.558 |
| SMC |
15 |
0.859 |
0.397 |
0.370 |
| SMC |
18 |
1.067 |
0.293 |
0.421 |
| Metro |
5 |
7.771 |
1.66e-07 |
9.658 |
| Metro |
8 |
5.339 |
3.63e-05 |
17.163 |
| Metro |
10 |
5.035 |
7.32e-05 |
42.497 |
| Metro |
12 |
17.283 |
4.13e-13 |
86.730 |
| Metro |
15 |
224.896 |
2.59e-42 |
138.677 |
| Metro |
18 |
198.760 |
5.53e-49 |
88.673 |
| DEMetro_Z |
5 |
20.542 |
1.96e-14 |
4008.726 |
| DEMetro_Z |
8 |
25.221 |
4.52e-16 |
1230.166 |
| DEMetro_Z |
10 |
30.005 |
1.8e-17 |
1496.788 |
| DEMetro_Z |
12 |
28.737 |
4.02e-17 |
1009.386 |
| DEMetro_Z |
15 |
20.388 |
2.24e-14 |
1145.082 |
| DEMetro_Z |
18 |
30.489 |
1.33e-17 |
613.855 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-20.517
|
2e-14
|
-4.588
|
| HMC_vs_DEMetro_Z |
1
|
-23.566
|
1.58e-15
|
-5.269
|
| HMC_vs_DEMetro_Z |
2
|
-27.845
|
7.24e-17
|
-6.226
|
| HMC_vs_DEMetro_Z |
3
|
-25.911
|
2.75e-16
|
-5.794
|
| HMC_vs_DEMetro_Z |
4
|
-17.909
|
2.35e-13
|
-4.005
|
| HMC_vs_DEMetro_Z |
5
|
-26.049
|
2.49e-16
|
-5.825
|
| Metro_vs_SMC |
0
|
7.577
|
3.72e-07
|
1.694
|
| Metro_vs_SMC |
1
|
5.485
|
2.73e-05
|
1.226
|
| Metro_vs_SMC |
2
|
4.997
|
8.01e-05
|
1.117
|
| Metro_vs_SMC |
3
|
17.580
|
3.27e-13
|
3.931
|
| Metro_vs_SMC |
4
|
218.020
|
9.38e-34
|
48.751
|
| Metro_vs_SMC |
5
|
184.201
|
2.3e-32
|
41.189
|
| Metro_vs_DEMetro_Z |
0
|
-20.440
|
2.14e-14
|
-4.570
|
| Metro_vs_DEMetro_Z |
1
|
-24.736
|
6.48e-16
|
-5.531
|
| Metro_vs_DEMetro_Z |
2
|
-29.580
|
2.35e-17
|
-6.614
|
| Metro_vs_DEMetro_Z |
3
|
-25.219
|
4.53e-16
|
-5.639
|
| Metro_vs_DEMetro_Z |
4
|
-17.923
|
2.31e-13
|
-4.008
|
| Metro_vs_DEMetro_Z |
5
|
-26.088
|
2.42e-16
|
-5.834
|
| HMC_vs_Metro |
0
|
-4.790
|
0.000127
|
-1.071
|
| HMC_vs_Metro |
1
|
5.135
|
5.89e-05
|
1.148
|
| HMC_vs_Metro |
2
|
8.028
|
1.59e-07
|
1.795
|
| HMC_vs_Metro |
3
|
2.257
|
0.036
|
0.505
|
| HMC_vs_Metro |
4
|
0.744
|
0.466
|
0.166
|
| HMC_vs_Metro |
5
|
1.243
|
0.229
|
0.278
|
| HMC_vs_SMC |
0
|
1.893
|
0.0737
|
0.423
|
| HMC_vs_SMC |
1
|
7.797
|
2.45e-07
|
1.744
|
| HMC_vs_SMC |
2
|
275.816
|
1.08e-35
|
61.674
|
| HMC_vs_SMC |
3
|
342.612
|
1.75e-37
|
76.610
|
| HMC_vs_SMC |
4
|
218.875
|
8.7e-34
|
48.942
|
| HMC_vs_SMC |
5
|
179.093
|
3.93e-32
|
40.046
|
| DEMetro_Z_vs_SMC |
0
|
20.538
|
1.97e-14
|
4.592
|
| DEMetro_Z_vs_SMC |
1
|
25.242
|
4.46e-16
|
5.644
|
| DEMetro_Z_vs_SMC |
2
|
30.006
|
1.8e-17
|
6.710
|
| DEMetro_Z_vs_SMC |
3
|
28.725
|
4.06e-17
|
6.423
|
| DEMetro_Z_vs_SMC |
4
|
20.352
|
2.32e-14
|
4.551
|
| DEMetro_Z_vs_SMC |
5
|
30.591
|
1.26e-17
|
6.840
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.030 |
0.024 |
0.003 |
2.294 |
| HMC |
8 |
0.479 |
0.028 |
0.008 |
54.973 |
| HMC |
10 |
0.922 |
0.029 |
0.008 |
109.440 |
| HMC |
12 |
1.102 |
0.033 |
0.011 |
98.020 |
| HMC |
15 |
1.372 |
0.032 |
0.010 |
138.777 |
| HMC |
18 |
1.637 |
0.038 |
0.018 |
88.752 |
| SMC |
5 |
0.025 |
0.024 |
0.003 |
0.497 |
| SMC |
8 |
0.025 |
0.028 |
0.008 |
-0.450 |
| SMC |
10 |
0.032 |
0.029 |
0.008 |
0.282 |
| SMC |
12 |
0.027 |
0.033 |
0.011 |
-0.558 |
| SMC |
15 |
0.035 |
0.032 |
0.010 |
0.370 |
| SMC |
18 |
0.045 |
0.038 |
0.018 |
0.421 |
| Metro |
5 |
0.049 |
0.024 |
0.003 |
9.658 |
| Metro |
8 |
0.169 |
0.028 |
0.008 |
17.163 |
| Metro |
10 |
0.376 |
0.029 |
0.008 |
42.497 |
| Metro |
12 |
0.979 |
0.033 |
0.011 |
86.730 |
| Metro |
15 |
1.371 |
0.032 |
0.010 |
138.677 |
| Metro |
18 |
1.636 |
0.038 |
0.018 |
88.673 |
| DEMetro_Z |
5 |
10.614 |
0.024 |
0.003 |
4008.726 |
| DEMetro_Z |
8 |
10.115 |
0.028 |
0.008 |
1230.166 |
| DEMetro_Z |
10 |
12.236 |
0.029 |
0.008 |
1496.788 |
| DEMetro_Z |
12 |
11.036 |
0.033 |
0.011 |
1009.386 |
| DEMetro_Z |
15 |
11.091 |
0.032 |
0.010 |
1145.082 |
| DEMetro_Z |
18 |
11.100 |
0.038 |
0.018 |
613.855 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.502 |
0.0182 |
0.634 |
| HMC |
8 |
5.825 |
1.3e-05 |
75.922 |
| HMC |
10 |
470.056 |
8.94e-55 |
243.979 |
| HMC |
12 |
717.825 |
1.7e-75 |
264.721 |
| HMC |
15 |
747.176 |
1.07e-60 |
383.077 |
| HMC |
18 |
1213.905 |
5.14e-72 |
551.127 |
| SMC |
5 |
-1.330 |
0.192 |
-0.378 |
| SMC |
8 |
-1.934 |
0.065 |
-0.461 |
| SMC |
10 |
0.741 |
0.463 |
0.227 |
| SMC |
12 |
-0.485 |
0.631 |
-0.135 |
| SMC |
15 |
1.865 |
0.0715 |
0.787 |
| SMC |
18 |
1.479 |
0.148 |
0.557 |
| Metro |
5 |
6.206 |
3.04e-07 |
2.045 |
| Metro |
8 |
2.781 |
0.0118 |
9.581 |
| Metro |
10 |
3.451 |
0.00268 |
65.644 |
| Metro |
12 |
12.050 |
2.41e-10 |
221.909 |
| Metro |
15 |
748.563 |
8.93e-61 |
383.201 |
| Metro |
18 |
1191.530 |
7.43e-71 |
551.047 |
| DEMetro_Z |
5 |
16.154 |
1.48e-12 |
2130.037 |
| DEMetro_Z |
8 |
17.224 |
4.73e-13 |
1121.562 |
| DEMetro_Z |
10 |
11.197 |
8.27e-10 |
1186.216 |
| DEMetro_Z |
12 |
12.516 |
1.27e-10 |
852.201 |
| DEMetro_Z |
15 |
19.452 |
5.27e-14 |
802.504 |
| DEMetro_Z |
18 |
19.532 |
4.89e-14 |
978.110 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
4.914
|
9.63e-05
|
1.099
|
| HMC_vs_SMC |
1
|
5.874
|
1.17e-05
|
1.313
|
| HMC_vs_SMC |
2
|
497.707
|
1.45e-40
|
111.291
|
| HMC_vs_SMC |
3
|
692.991
|
2.7e-43
|
154.958
|
| HMC_vs_SMC |
4
|
893.937
|
2.14e-45
|
199.890
|
| HMC_vs_SMC |
5
|
1057.127
|
8.84e-47
|
236.381
|
| Metro_vs_DEMetro_Z |
0
|
-16.145
|
1.5e-12
|
-3.610
|
| Metro_vs_DEMetro_Z |
1
|
-17.022
|
5.84e-13
|
-3.806
|
| Metro_vs_DEMetro_Z |
2
|
-10.105
|
4.44e-09
|
-2.260
|
| Metro_vs_DEMetro_Z |
3
|
-9.009
|
2.75e-08
|
-2.014
|
| Metro_vs_DEMetro_Z |
4
|
-10.191
|
3.88e-09
|
-2.279
|
| Metro_vs_DEMetro_Z |
5
|
-8.530
|
6.39e-08
|
-1.907
|
| HMC_vs_Metro |
0
|
-5.903
|
1.1e-05
|
-1.320
|
| HMC_vs_Metro |
1
|
5.062
|
6.92e-05
|
1.132
|
| HMC_vs_Metro |
2
|
9.373
|
1.48e-08
|
2.096
|
| HMC_vs_Metro |
3
|
2.310
|
0.0323
|
0.517
|
| HMC_vs_Metro |
4
|
-1.264
|
0.221
|
-0.283
|
| HMC_vs_Metro |
5
|
0.737
|
0.47
|
0.165
|
| HMC_vs_DEMetro_Z |
0
|
-16.154
|
1.48e-12
|
-3.612
|
| HMC_vs_DEMetro_Z |
1
|
-16.229
|
1.37e-12
|
-3.629
|
| HMC_vs_DEMetro_Z |
2
|
-8.904
|
3.3e-08
|
-1.991
|
| HMC_vs_DEMetro_Z |
3
|
-8.631
|
5.33e-08
|
-1.930
|
| HMC_vs_DEMetro_Z |
4
|
-10.200
|
3.82e-09
|
-2.281
|
| HMC_vs_DEMetro_Z |
5
|
-8.525
|
6.44e-08
|
-1.906
|
| Metro_vs_SMC |
0
|
8.150
|
1.27e-07
|
1.822
|
| Metro_vs_SMC |
1
|
2.950
|
0.00823
|
0.660
|
| Metro_vs_SMC |
2
|
3.447
|
0.0027
|
0.771
|
| Metro_vs_SMC |
3
|
12.070
|
2.35e-10
|
2.699
|
| Metro_vs_SMC |
4
|
902.145
|
1.8e-45
|
201.726
|
| Metro_vs_SMC |
5
|
1047.650
|
1.05e-46
|
234.262
|
| DEMetro_Z_vs_SMC |
0
|
16.162
|
1.47e-12
|
3.614
|
| DEMetro_Z_vs_SMC |
1
|
17.239
|
4.65e-13
|
3.855
|
| DEMetro_Z_vs_SMC |
2
|
11.194
|
8.31e-10
|
2.503
|
| DEMetro_Z_vs_SMC |
3
|
12.520
|
1.26e-10
|
2.800
|
| DEMetro_Z_vs_SMC |
4
|
19.451
|
5.28e-14
|
4.349
|
| DEMetro_Z_vs_SMC |
5
|
19.525
|
4.93e-14
|
4.366
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.045 |
0.039 |
0.009 |
0.634 |
| HMC |
8 |
1.607 |
0.048 |
0.021 |
75.922 |
| HMC |
10 |
4.573 |
0.049 |
0.019 |
243.979 |
| HMC |
12 |
6.557 |
0.053 |
0.025 |
264.721 |
| HMC |
15 |
10.283 |
0.053 |
0.027 |
383.077 |
| HMC |
18 |
14.784 |
0.057 |
0.027 |
551.127 |
| SMC |
5 |
0.035 |
0.039 |
0.009 |
-0.378 |
| SMC |
8 |
0.039 |
0.048 |
0.021 |
-0.461 |
| SMC |
10 |
0.053 |
0.049 |
0.019 |
0.227 |
| SMC |
12 |
0.050 |
0.053 |
0.025 |
-0.135 |
| SMC |
15 |
0.074 |
0.053 |
0.027 |
0.787 |
| SMC |
18 |
0.072 |
0.057 |
0.027 |
0.557 |
| Metro |
5 |
0.058 |
0.039 |
0.009 |
2.045 |
| Metro |
8 |
0.245 |
0.048 |
0.021 |
9.581 |
| Metro |
10 |
1.266 |
0.049 |
0.019 |
65.644 |
| Metro |
12 |
5.505 |
0.053 |
0.025 |
221.909 |
| Metro |
15 |
10.286 |
0.053 |
0.027 |
383.201 |
| Metro |
18 |
14.781 |
0.057 |
0.027 |
551.047 |
| DEMetro_Z |
5 |
19.939 |
0.039 |
0.009 |
2130.037 |
| DEMetro_Z |
8 |
23.083 |
0.048 |
0.021 |
1121.562 |
| DEMetro_Z |
10 |
22.043 |
0.049 |
0.019 |
1186.216 |
| DEMetro_Z |
12 |
20.990 |
0.053 |
0.025 |
852.201 |
| DEMetro_Z |
15 |
21.483 |
0.053 |
0.027 |
802.504 |
| DEMetro_Z |
18 |
26.193 |
0.057 |
0.027 |
978.110 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.271 |
0.00353 |
2.802 |
| HMC |
8 |
7.427 |
4.93e-07 |
72.986 |
| HMC |
10 |
121.235 |
1.02e-30 |
140.526 |
| HMC |
12 |
102.063 |
3.97e-29 |
120.570 |
| HMC |
15 |
68.755 |
1.5e-24 |
172.027 |
| HMC |
18 |
99.200 |
3.3e-29 |
106.989 |
| SMC |
5 |
0.851 |
0.401 |
0.319 |
| SMC |
8 |
-1.369 |
0.18 |
-0.392 |
| SMC |
10 |
0.977 |
0.335 |
0.331 |
| SMC |
12 |
-1.658 |
0.106 |
-0.484 |
| SMC |
15 |
0.962 |
0.344 |
0.463 |
| SMC |
18 |
1.067 |
0.293 |
0.425 |
| Metro |
5 |
8.027 |
1.04e-07 |
10.394 |
| Metro |
8 |
5.056 |
6.91e-05 |
21.891 |
| Metro |
10 |
4.998 |
7.96e-05 |
52.868 |
| Metro |
12 |
16.558 |
9.15e-13 |
105.001 |
| Metro |
15 |
109.688 |
5.1e-29 |
172.976 |
| Metro |
18 |
81.425 |
7.67e-27 |
106.810 |
| DEMetro_Z |
5 |
19.638 |
4.44e-14 |
4983.352 |
| DEMetro_Z |
8 |
23.879 |
1.24e-15 |
1706.816 |
| DEMetro_Z |
10 |
32.464 |
4.15e-18 |
1986.233 |
| DEMetro_Z |
12 |
28.736 |
4.03e-17 |
1285.716 |
| DEMetro_Z |
15 |
21.057 |
1.25e-14 |
1504.518 |
| DEMetro_Z |
18 |
30.043 |
1.75e-17 |
768.712 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-19.556
|
4.79e-14
|
-4.373
|
| Metro_vs_DEMetro_Z |
1
|
-23.389
|
1.82e-15
|
-5.230
|
| Metro_vs_DEMetro_Z |
2
|
-32.408
|
4.29e-18
|
-7.247
|
| Metro_vs_DEMetro_Z |
3
|
-25.414
|
3.93e-16
|
-5.683
|
| Metro_vs_DEMetro_Z |
4
|
-18.521
|
1.28e-13
|
-4.141
|
| Metro_vs_DEMetro_Z |
5
|
-25.636
|
3.35e-16
|
-5.732
|
| DEMetro_Z_vs_SMC |
0
|
19.633
|
4.46e-14
|
4.390
|
| DEMetro_Z_vs_SMC |
1
|
23.894
|
1.23e-15
|
5.343
|
| DEMetro_Z_vs_SMC |
2
|
32.454
|
4.18e-18
|
7.257
|
| DEMetro_Z_vs_SMC |
3
|
28.724
|
4.06e-17
|
6.423
|
| DEMetro_Z_vs_SMC |
4
|
21.019
|
1.29e-14
|
4.700
|
| DEMetro_Z_vs_SMC |
5
|
30.106
|
1.69e-17
|
6.732
|
| HMC_vs_DEMetro_Z |
0
|
-19.619
|
4.52e-14
|
-4.387
|
| HMC_vs_DEMetro_Z |
1
|
-22.312
|
4.32e-15
|
-4.989
|
| HMC_vs_DEMetro_Z |
2
|
-30.065
|
1.74e-17
|
-6.723
|
| HMC_vs_DEMetro_Z |
3
|
-25.952
|
2.67e-16
|
-5.803
|
| HMC_vs_DEMetro_Z |
4
|
-18.520
|
1.28e-13
|
-4.141
|
| HMC_vs_DEMetro_Z |
5
|
-25.710
|
3.17e-16
|
-5.749
|
| HMC_vs_Metro |
0
|
-4.746
|
0.000141
|
-1.061
|
| HMC_vs_Metro |
1
|
4.964
|
8.62e-05
|
1.110
|
| HMC_vs_Metro |
2
|
7.946
|
1.85e-07
|
1.777
|
| HMC_vs_Metro |
3
|
2.546
|
0.0197
|
0.569
|
| HMC_vs_Metro |
4
|
-0.408
|
0.688
|
-0.091
|
| HMC_vs_Metro |
5
|
0.102
|
0.919
|
0.023
|
| HMC_vs_SMC |
0
|
2.784
|
0.0118
|
0.623
|
| HMC_vs_SMC |
1
|
7.468
|
4.58e-07
|
1.670
|
| HMC_vs_SMC |
2
|
129.656
|
1.81e-29
|
28.992
|
| HMC_vs_SMC |
3
|
108.733
|
5.1e-28
|
24.313
|
| HMC_vs_SMC |
4
|
73.350
|
8.88e-25
|
16.402
|
| HMC_vs_SMC |
5
|
90.006
|
1.84e-26
|
20.126
|
| Metro_vs_SMC |
0
|
7.927
|
1.92e-07
|
1.772
|
| Metro_vs_SMC |
1
|
5.149
|
5.71e-05
|
1.151
|
| Metro_vs_SMC |
2
|
4.966
|
8.57e-05
|
1.110
|
| Metro_vs_SMC |
3
|
16.757
|
7.73e-13
|
3.747
|
| Metro_vs_SMC |
4
|
111.704
|
3.06e-28
|
24.978
|
| Metro_vs_SMC |
5
|
81.382
|
1.24e-25
|
18.198
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.036 |
0.031 |
0.002 |
2.802 |
| HMC |
8 |
0.391 |
0.035 |
0.005 |
72.986 |
| HMC |
10 |
0.747 |
0.036 |
0.005 |
140.526 |
| HMC |
12 |
0.894 |
0.040 |
0.007 |
120.570 |
| HMC |
15 |
1.100 |
0.040 |
0.006 |
172.027 |
| HMC |
18 |
1.330 |
0.044 |
0.012 |
106.989 |
| SMC |
5 |
0.032 |
0.031 |
0.002 |
0.319 |
| SMC |
8 |
0.033 |
0.035 |
0.005 |
-0.392 |
| SMC |
10 |
0.038 |
0.036 |
0.005 |
0.331 |
| SMC |
12 |
0.036 |
0.040 |
0.007 |
-0.484 |
| SMC |
15 |
0.043 |
0.040 |
0.006 |
0.463 |
| SMC |
18 |
0.049 |
0.044 |
0.012 |
0.425 |
| Metro |
5 |
0.049 |
0.031 |
0.002 |
10.394 |
| Metro |
8 |
0.142 |
0.035 |
0.005 |
21.891 |
| Metro |
10 |
0.304 |
0.036 |
0.005 |
52.868 |
| Metro |
12 |
0.783 |
0.040 |
0.007 |
105.001 |
| Metro |
15 |
1.106 |
0.040 |
0.006 |
172.976 |
| Metro |
18 |
1.328 |
0.044 |
0.012 |
106.810 |
| DEMetro_Z |
5 |
8.865 |
0.031 |
0.002 |
4983.352 |
| DEMetro_Z |
8 |
8.374 |
0.035 |
0.005 |
1706.816 |
| DEMetro_Z |
10 |
10.083 |
0.036 |
0.005 |
1986.233 |
| DEMetro_Z |
12 |
9.148 |
0.040 |
0.007 |
1285.716 |
| DEMetro_Z |
15 |
9.314 |
0.040 |
0.006 |
1504.518 |
| DEMetro_Z |
18 |
9.282 |
0.044 |
0.012 |
768.712 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.422 |
0.00246 |
2.884 |
| HMC |
8 |
7.806 |
2.39e-07 |
69.128 |
| HMC |
10 |
111.252 |
5.21e-30 |
127.106 |
| HMC |
12 |
127.701 |
2.52e-32 |
117.169 |
| HMC |
15 |
139.229 |
6.37e-32 |
162.480 |
| HMC |
18 |
131.076 |
2.83e-33 |
108.726 |
| SMC |
5 |
1.595 |
0.119 |
0.570 |
| SMC |
8 |
-1.454 |
0.154 |
-0.438 |
| SMC |
10 |
0.945 |
0.351 |
0.320 |
| SMC |
12 |
-1.840 |
0.0736 |
-0.559 |
| SMC |
15 |
1.038 |
0.307 |
0.422 |
| SMC |
18 |
0.983 |
0.333 |
0.408 |
| Metro |
5 |
8.308 |
5.76e-08 |
10.170 |
| Metro |
8 |
5.333 |
3.72e-05 |
21.137 |
| Metro |
10 |
4.870 |
0.000106 |
48.566 |
| Metro |
12 |
16.994 |
5.72e-13 |
102.950 |
| Metro |
15 |
159.644 |
8.63e-34 |
161.975 |
| Metro |
18 |
124.729 |
1.88e-32 |
108.563 |
| DEMetro_Z |
5 |
88.072 |
2.57e-26 |
697.737 |
| DEMetro_Z |
8 |
68.305 |
2.74e-24 |
302.495 |
| DEMetro_Z |
10 |
97.716 |
2.2e-27 |
291.298 |
| DEMetro_Z |
12 |
53.518 |
2.88e-22 |
247.951 |
| DEMetro_Z |
15 |
68.061 |
2.92e-24 |
296.984 |
| DEMetro_Z |
18 |
77.531 |
1.42e-25 |
187.566 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
87.345
|
3.25e-26
|
19.531
|
| DEMetro_Z_vs_SMC |
1
|
68.546
|
3.2e-24
|
15.327
|
| DEMetro_Z_vs_SMC |
2
|
98.352
|
3.42e-27
|
21.992
|
| DEMetro_Z_vs_SMC |
3
|
53.936
|
2.98e-22
|
12.061
|
| DEMetro_Z_vs_SMC |
4
|
67.227
|
4.63e-24
|
15.033
|
| DEMetro_Z_vs_SMC |
5
|
79.725
|
1.83e-25
|
17.827
|
| HMC_vs_Metro |
0
|
-4.679
|
0.000164
|
-1.046
|
| HMC_vs_Metro |
1
|
5.288
|
4.2e-05
|
1.182
|
| HMC_vs_Metro |
2
|
8.099
|
1.4e-07
|
1.811
|
| HMC_vs_Metro |
3
|
2.343
|
0.0301
|
0.524
|
| HMC_vs_Metro |
4
|
0.517
|
0.611
|
0.116
|
| HMC_vs_Metro |
5
|
0.192
|
0.85
|
0.043
|
| Metro_vs_DEMetro_Z |
0
|
-81.076
|
1.33e-25
|
-18.129
|
| Metro_vs_DEMetro_Z |
1
|
-48.690
|
2.05e-21
|
-10.887
|
| Metro_vs_DEMetro_Z |
2
|
-25.309
|
4.24e-16
|
-5.659
|
| Metro_vs_DEMetro_Z |
3
|
-17.962
|
2.23e-13
|
-4.016
|
| Metro_vs_DEMetro_Z |
4
|
-31.605
|
6.85e-18
|
-7.067
|
| Metro_vs_DEMetro_Z |
5
|
-27.617
|
8.43e-17
|
-6.175
|
| HMC_vs_SMC |
0
|
2.625
|
0.0167
|
0.587
|
| HMC_vs_SMC |
1
|
7.854
|
2.2e-07
|
1.756
|
| HMC_vs_SMC |
2
|
112.733
|
2.57e-28
|
25.208
|
| HMC_vs_SMC |
3
|
139.649
|
4.42e-30
|
31.227
|
| HMC_vs_SMC |
4
|
142.443
|
3.03e-30
|
31.851
|
| HMC_vs_SMC |
5
|
112.882
|
2.51e-28
|
25.241
|
| Metro_vs_SMC |
0
|
7.980
|
1.74e-07
|
1.784
|
| Metro_vs_SMC |
1
|
5.449
|
2.95e-05
|
1.218
|
| Metro_vs_SMC |
2
|
4.843
|
0.000113
|
1.083
|
| Metro_vs_SMC |
3
|
17.219
|
4.75e-13
|
3.850
|
| Metro_vs_SMC |
4
|
143.876
|
2.51e-30
|
32.172
|
| Metro_vs_SMC |
5
|
115.141
|
1.72e-28
|
25.746
|
| HMC_vs_DEMetro_Z |
0
|
-85.040
|
5.39e-26
|
-19.016
|
| HMC_vs_DEMetro_Z |
1
|
-23.838
|
1.28e-15
|
-5.330
|
| HMC_vs_DEMetro_Z |
2
|
-61.813
|
2.26e-23
|
-13.822
|
| HMC_vs_DEMetro_Z |
3
|
-27.424
|
9.61e-17
|
-6.132
|
| HMC_vs_DEMetro_Z |
4
|
-33.739
|
2.02e-18
|
-7.544
|
| HMC_vs_DEMetro_Z |
5
|
-27.492
|
9.17e-17
|
-6.147
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.017 |
0.013 |
0.001 |
2.884 |
| HMC |
8 |
0.220 |
0.014 |
0.003 |
69.128 |
| HMC |
10 |
0.408 |
0.014 |
0.003 |
127.106 |
| HMC |
12 |
0.457 |
0.015 |
0.004 |
117.169 |
| HMC |
15 |
0.512 |
0.012 |
0.003 |
162.480 |
| HMC |
18 |
0.543 |
0.013 |
0.005 |
108.726 |
| SMC |
5 |
0.014 |
0.013 |
0.001 |
0.570 |
| SMC |
8 |
0.013 |
0.014 |
0.003 |
-0.438 |
| SMC |
10 |
0.015 |
0.014 |
0.003 |
0.320 |
| SMC |
12 |
0.013 |
0.015 |
0.004 |
-0.559 |
| SMC |
15 |
0.014 |
0.012 |
0.003 |
0.422 |
| SMC |
18 |
0.015 |
0.013 |
0.005 |
0.408 |
| Metro |
5 |
0.027 |
0.013 |
0.001 |
10.170 |
| Metro |
8 |
0.077 |
0.014 |
0.003 |
21.137 |
| Metro |
10 |
0.164 |
0.014 |
0.003 |
48.566 |
| Metro |
12 |
0.403 |
0.015 |
0.004 |
102.950 |
| Metro |
15 |
0.510 |
0.012 |
0.003 |
161.975 |
| Metro |
18 |
0.542 |
0.013 |
0.005 |
108.563 |
| DEMetro_Z |
5 |
0.921 |
0.013 |
0.001 |
697.737 |
| DEMetro_Z |
8 |
0.915 |
0.014 |
0.003 |
302.495 |
| DEMetro_Z |
10 |
0.916 |
0.014 |
0.003 |
291.298 |
| DEMetro_Z |
12 |
0.951 |
0.015 |
0.004 |
247.951 |
| DEMetro_Z |
15 |
0.925 |
0.012 |
0.003 |
296.984 |
| DEMetro_Z |
18 |
0.927 |
0.013 |
0.005 |
187.566 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Correlation
(Mixture,
mm,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.189 |
5.19e-05 |
38.891 |
| HMC |
8 |
4.199 |
0.000484 |
26.345 |
| HMC |
10 |
3.628 |
0.00178 |
17.931 |
| HMC |
12 |
4.425 |
0.000286 |
17.304 |
| HMC |
15 |
5.066 |
6.84e-05 |
43.335 |
| HMC |
18 |
6.006 |
8.72e-06 |
29.855 |
| SMC |
5 |
0.479 |
0.635 |
0.169 |
| SMC |
8 |
1.316 |
0.197 |
0.485 |
| SMC |
10 |
0.772 |
0.445 |
0.221 |
| SMC |
12 |
-0.229 |
0.82 |
-0.065 |
| SMC |
15 |
1.510 |
0.142 |
0.766 |
| SMC |
18 |
-0.057 |
0.955 |
-0.017 |
| Metro |
5 |
6.916 |
1.3e-06 |
24.693 |
| Metro |
8 |
5.663 |
1.83e-05 |
29.591 |
| Metro |
10 |
4.332 |
0.000358 |
27.294 |
| Metro |
12 |
5.245 |
4.47e-05 |
17.042 |
| Metro |
15 |
4.761 |
0.000136 |
41.259 |
| Metro |
18 |
6.819 |
1.61e-06 |
31.659 |
| DEMetro_Z |
5 |
5.787 |
1.4e-05 |
30.721 |
| DEMetro_Z |
8 |
7.917 |
1.89e-07 |
36.514 |
| DEMetro_Z |
10 |
5.275 |
4.25e-05 |
23.689 |
| DEMetro_Z |
12 |
5.050 |
7.01e-05 |
23.056 |
| DEMetro_Z |
15 |
7.869 |
2.12e-07 |
65.297 |
| DEMetro_Z |
18 |
8.861 |
3.38e-08 |
35.355 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
0.840
|
0.411
|
0.188
|
| HMC_vs_DEMetro_Z |
1
|
-1.368
|
0.187
|
-0.306
|
| HMC_vs_DEMetro_Z |
2
|
-0.960
|
0.349
|
-0.215
|
| HMC_vs_DEMetro_Z |
3
|
-0.974
|
0.342
|
-0.218
|
| HMC_vs_DEMetro_Z |
4
|
-1.813
|
0.0857
|
-0.405
|
| HMC_vs_DEMetro_Z |
5
|
-0.782
|
0.444
|
-0.175
|
| Metro_vs_SMC |
0
|
6.741
|
1.93e-06
|
1.507
|
| Metro_vs_SMC |
1
|
5.622
|
2.02e-05
|
1.257
|
| Metro_vs_SMC |
2
|
4.291
|
0.000394
|
0.959
|
| Metro_vs_SMC |
3
|
5.281
|
4.26e-05
|
1.181
|
| Metro_vs_SMC |
4
|
4.652
|
0.000174
|
1.040
|
| Metro_vs_SMC |
5
|
6.891
|
1.43e-06
|
1.541
|
| Metro_vs_DEMetro_Z |
0
|
-1.027
|
0.317
|
-0.230
|
| Metro_vs_DEMetro_Z |
1
|
-1.206
|
0.243
|
-0.270
|
| Metro_vs_DEMetro_Z |
2
|
0.505
|
0.62
|
0.113
|
| Metro_vs_DEMetro_Z |
3
|
-1.104
|
0.283
|
-0.247
|
| Metro_vs_DEMetro_Z |
4
|
-2.101
|
0.0492
|
-0.470
|
| Metro_vs_DEMetro_Z |
5
|
-0.619
|
0.543
|
-0.138
|
| HMC_vs_Metro |
0
|
2.220
|
0.0388
|
0.496
|
| HMC_vs_Metro |
1
|
-0.465
|
0.647
|
-0.104
|
| HMC_vs_Metro |
2
|
-1.640
|
0.118
|
-0.367
|
| HMC_vs_Metro |
3
|
0.063
|
0.951
|
0.014
|
| HMC_vs_Metro |
4
|
0.225
|
0.825
|
0.050
|
| HMC_vs_Metro |
5
|
-0.411
|
0.685
|
-0.092
|
| HMC_vs_SMC |
0
|
5.168
|
5.47e-05
|
1.156
|
| HMC_vs_SMC |
1
|
4.198
|
0.000487
|
0.939
|
| HMC_vs_SMC |
2
|
3.601
|
0.0019
|
0.805
|
| HMC_vs_SMC |
3
|
4.502
|
0.000244
|
1.007
|
| HMC_vs_SMC |
4
|
4.937
|
9.14e-05
|
1.104
|
| HMC_vs_SMC |
5
|
6.164
|
6.35e-06
|
1.378
|
| DEMetro_Z_vs_SMC |
0
|
5.863
|
1.2e-05
|
1.311
|
| DEMetro_Z_vs_SMC |
1
|
7.851
|
2.21e-07
|
1.755
|
| DEMetro_Z_vs_SMC |
2
|
5.261
|
4.45e-05
|
1.176
|
| DEMetro_Z_vs_SMC |
3
|
5.091
|
6.5e-05
|
1.138
|
| DEMetro_Z_vs_SMC |
4
|
7.600
|
3.56e-07
|
1.699
|
| DEMetro_Z_vs_SMC |
5
|
8.700
|
4.72e-08
|
1.945
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.771 |
0.034 |
0.019 |
38.891 |
| HMC |
8 |
0.925 |
0.047 |
0.033 |
26.345 |
| HMC |
10 |
0.903 |
0.048 |
0.048 |
17.931 |
| HMC |
12 |
1.305 |
0.088 |
0.070 |
17.304 |
| HMC |
15 |
2.163 |
0.073 |
0.048 |
43.335 |
| HMC |
18 |
3.034 |
0.135 |
0.097 |
29.855 |
| SMC |
5 |
0.038 |
0.034 |
0.019 |
0.169 |
| SMC |
8 |
0.063 |
0.047 |
0.033 |
0.485 |
| SMC |
10 |
0.059 |
0.048 |
0.048 |
0.221 |
| SMC |
12 |
0.083 |
0.088 |
0.070 |
-0.065 |
| SMC |
15 |
0.110 |
0.073 |
0.048 |
0.766 |
| SMC |
18 |
0.133 |
0.135 |
0.097 |
-0.017 |
| Metro |
5 |
0.502 |
0.034 |
0.019 |
24.693 |
| Metro |
8 |
1.033 |
0.047 |
0.033 |
29.591 |
| Metro |
10 |
1.349 |
0.048 |
0.048 |
27.294 |
| Metro |
12 |
1.287 |
0.088 |
0.070 |
17.042 |
| Metro |
15 |
2.063 |
0.073 |
0.048 |
41.259 |
| Metro |
18 |
3.209 |
0.135 |
0.097 |
31.659 |
| DEMetro_Z |
5 |
0.617 |
0.034 |
0.019 |
30.721 |
| DEMetro_Z |
8 |
1.264 |
0.047 |
0.033 |
36.514 |
| DEMetro_Z |
10 |
1.178 |
0.048 |
0.048 |
23.689 |
| DEMetro_Z |
12 |
1.710 |
0.088 |
0.070 |
23.056 |
| DEMetro_Z |
15 |
3.223 |
0.073 |
0.048 |
65.297 |
| DEMetro_Z |
18 |
3.568 |
0.135 |
0.097 |
35.355 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.925 |
0.000906 |
30.207 |
| HMC |
8 |
3.220 |
0.00451 |
29.367 |
| HMC |
10 |
2.876 |
0.00968 |
30.943 |
| HMC |
12 |
3.430 |
0.00281 |
47.628 |
| HMC |
15 |
3.709 |
0.00149 |
75.362 |
| HMC |
18 |
4.215 |
0.000469 |
125.265 |
| SMC |
5 |
-1.089 |
0.283 |
-0.343 |
| SMC |
8 |
1.176 |
0.247 |
0.396 |
| SMC |
10 |
0.712 |
0.481 |
0.273 |
| SMC |
12 |
1.113 |
0.273 |
0.420 |
| SMC |
15 |
-0.832 |
0.411 |
-0.255 |
| SMC |
18 |
1.509 |
0.14 |
0.555 |
| Metro |
5 |
4.922 |
9.05e-05 |
12.179 |
| Metro |
8 |
4.354 |
0.00034 |
28.872 |
| Metro |
10 |
3.600 |
0.00191 |
61.617 |
| Metro |
12 |
6.271 |
5.02e-06 |
43.962 |
| Metro |
15 |
3.630 |
0.00178 |
74.158 |
| Metro |
18 |
4.529 |
0.00023 |
130.892 |
| DEMetro_Z |
5 |
3.409 |
0.00293 |
19.450 |
| DEMetro_Z |
8 |
4.206 |
0.000477 |
35.230 |
| DEMetro_Z |
10 |
3.702 |
0.00151 |
39.092 |
| DEMetro_Z |
12 |
3.732 |
0.00141 |
75.489 |
| DEMetro_Z |
15 |
5.283 |
4.24e-05 |
130.227 |
| DEMetro_Z |
18 |
5.135 |
5.88e-05 |
141.210 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.983
|
0.000796
|
0.891
|
| HMC_vs_SMC |
1
|
3.179
|
0.00494
|
0.711
|
| HMC_vs_SMC |
2
|
2.838
|
0.0105
|
0.635
|
| HMC_vs_SMC |
3
|
3.408
|
0.00295
|
0.762
|
| HMC_vs_SMC |
4
|
3.712
|
0.00148
|
0.830
|
| HMC_vs_SMC |
5
|
4.192
|
0.000495
|
0.937
|
| Metro_vs_DEMetro_Z |
0
|
-1.207
|
0.242
|
-0.270
|
| Metro_vs_DEMetro_Z |
1
|
-0.620
|
0.543
|
-0.139
|
| Metro_vs_DEMetro_Z |
2
|
1.173
|
0.255
|
0.262
|
| Metro_vs_DEMetro_Z |
3
|
-1.522
|
0.144
|
-0.340
|
| Metro_vs_DEMetro_Z |
4
|
-1.983
|
0.062
|
-0.443
|
| Metro_vs_DEMetro_Z |
5
|
-0.305
|
0.764
|
-0.068
|
| HMC_vs_Metro |
0
|
2.513
|
0.0212
|
0.562
|
| HMC_vs_Metro |
1
|
0.068
|
0.946
|
0.015
|
| HMC_vs_Metro |
2
|
-2.075
|
0.0518
|
-0.464
|
| HMC_vs_Metro |
3
|
0.264
|
0.794
|
0.059
|
| HMC_vs_Metro |
4
|
0.051
|
0.96
|
0.011
|
| HMC_vs_Metro |
5
|
-0.188
|
0.853
|
-0.042
|
| HMC_vs_DEMetro_Z |
0
|
1.088
|
0.29
|
0.243
|
| HMC_vs_DEMetro_Z |
1
|
-0.471
|
0.643
|
-0.105
|
| HMC_vs_DEMetro_Z |
2
|
-0.591
|
0.562
|
-0.132
|
| HMC_vs_DEMetro_Z |
3
|
-1.144
|
0.267
|
-0.256
|
| HMC_vs_DEMetro_Z |
4
|
-1.584
|
0.13
|
-0.354
|
| HMC_vs_DEMetro_Z |
5
|
-0.383
|
0.706
|
-0.086
|
| Metro_vs_SMC |
0
|
4.978
|
8.35e-05
|
1.113
|
| Metro_vs_SMC |
1
|
4.282
|
0.000403
|
0.957
|
| Metro_vs_SMC |
2
|
3.590
|
0.00195
|
0.803
|
| Metro_vs_SMC |
3
|
6.143
|
6.63e-06
|
1.374
|
| Metro_vs_SMC |
4
|
3.625
|
0.0018
|
0.810
|
| Metro_vs_SMC |
5
|
4.498
|
0.000246
|
1.006
|
| DEMetro_Z_vs_SMC |
0
|
3.466
|
0.00258
|
0.775
|
| DEMetro_Z_vs_SMC |
1
|
4.147
|
0.000548
|
0.927
|
| DEMetro_Z_vs_SMC |
2
|
3.632
|
0.00178
|
0.812
|
| DEMetro_Z_vs_SMC |
3
|
3.696
|
0.00153
|
0.826
|
| DEMetro_Z_vs_SMC |
4
|
5.281
|
4.26e-05
|
1.181
|
| DEMetro_Z_vs_SMC |
5
|
5.094
|
6.45e-05
|
1.139
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.375 |
0.077 |
0.043 |
30.207 |
| HMC |
8 |
2.451 |
0.089 |
0.080 |
29.367 |
| HMC |
10 |
2.759 |
0.120 |
0.085 |
30.943 |
| HMC |
12 |
4.558 |
0.141 |
0.093 |
47.628 |
| HMC |
15 |
11.123 |
0.205 |
0.145 |
75.362 |
| HMC |
18 |
19.326 |
0.184 |
0.153 |
125.265 |
| SMC |
5 |
0.062 |
0.077 |
0.043 |
-0.343 |
| SMC |
8 |
0.120 |
0.089 |
0.080 |
0.396 |
| SMC |
10 |
0.143 |
0.120 |
0.085 |
0.273 |
| SMC |
12 |
0.180 |
0.141 |
0.093 |
0.420 |
| SMC |
15 |
0.168 |
0.205 |
0.145 |
-0.255 |
| SMC |
18 |
0.269 |
0.184 |
0.153 |
0.555 |
| Metro |
5 |
0.601 |
0.077 |
0.043 |
12.179 |
| Metro |
8 |
2.412 |
0.089 |
0.080 |
28.872 |
| Metro |
10 |
5.375 |
0.120 |
0.085 |
61.617 |
| Metro |
12 |
4.218 |
0.141 |
0.093 |
43.962 |
| Metro |
15 |
10.949 |
0.205 |
0.145 |
74.158 |
| Metro |
18 |
20.186 |
0.184 |
0.153 |
130.892 |
| DEMetro_Z |
5 |
0.913 |
0.077 |
0.043 |
19.450 |
| DEMetro_Z |
8 |
2.923 |
0.089 |
0.080 |
35.230 |
| DEMetro_Z |
10 |
3.454 |
0.120 |
0.085 |
39.092 |
| DEMetro_Z |
12 |
7.141 |
0.141 |
0.093 |
75.489 |
| DEMetro_Z |
15 |
19.072 |
0.205 |
0.145 |
130.227 |
| DEMetro_Z |
18 |
21.762 |
0.184 |
0.153 |
141.210 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.087 |
6.52e-05 |
39.879 |
| HMC |
8 |
4.128 |
0.00057 |
31.457 |
| HMC |
10 |
3.622 |
0.00181 |
20.024 |
| HMC |
12 |
4.333 |
0.000355 |
18.108 |
| HMC |
15 |
5.038 |
7.28e-05 |
48.006 |
| HMC |
18 |
5.936 |
1.01e-05 |
31.268 |
| SMC |
5 |
-0.392 |
0.697 |
-0.129 |
| SMC |
8 |
1.856 |
0.0721 |
0.709 |
| SMC |
10 |
0.567 |
0.574 |
0.162 |
| SMC |
12 |
-0.168 |
0.868 |
-0.048 |
| SMC |
15 |
1.509 |
0.143 |
0.798 |
| SMC |
18 |
0.348 |
0.729 |
0.105 |
| Metro |
5 |
7.478 |
4.27e-07 |
26.519 |
| Metro |
8 |
5.758 |
1.49e-05 |
35.985 |
| Metro |
10 |
4.395 |
0.00031 |
31.281 |
| Metro |
12 |
5.534 |
2.38e-05 |
20.088 |
| Metro |
15 |
4.891 |
0.000101 |
48.320 |
| Metro |
18 |
7.075 |
9.61e-07 |
32.232 |
| DEMetro_Z |
5 |
6.191 |
5.9e-06 |
31.648 |
| DEMetro_Z |
8 |
7.524 |
4.03e-07 |
43.266 |
| DEMetro_Z |
10 |
5.473 |
2.75e-05 |
26.226 |
| DEMetro_Z |
12 |
5.085 |
6.5e-05 |
24.933 |
| DEMetro_Z |
15 |
7.545 |
3.93e-07 |
76.398 |
| DEMetro_Z |
18 |
8.963 |
2.84e-08 |
36.963 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.892
|
0.384
|
-0.199
|
| Metro_vs_DEMetro_Z |
1
|
-1.056
|
0.304
|
-0.236
|
| Metro_vs_DEMetro_Z |
2
|
0.628
|
0.538
|
0.140
|
| Metro_vs_DEMetro_Z |
3
|
-0.810
|
0.428
|
-0.181
|
| Metro_vs_DEMetro_Z |
4
|
-2.138
|
0.0457
|
-0.478
|
| Metro_vs_DEMetro_Z |
5
|
-0.770
|
0.451
|
-0.172
|
| DEMetro_Z_vs_SMC |
0
|
6.277
|
5.02e-06
|
1.403
|
| DEMetro_Z_vs_SMC |
1
|
7.373
|
5.51e-07
|
1.649
|
| DEMetro_Z_vs_SMC |
2
|
5.466
|
2.84e-05
|
1.222
|
| DEMetro_Z_vs_SMC |
3
|
5.098
|
6.39e-05
|
1.140
|
| DEMetro_Z_vs_SMC |
4
|
7.313
|
6.19e-07
|
1.635
|
| DEMetro_Z_vs_SMC |
5
|
8.747
|
4.35e-08
|
1.956
|
| HMC_vs_DEMetro_Z |
0
|
0.836
|
0.414
|
0.187
|
| HMC_vs_DEMetro_Z |
1
|
-1.261
|
0.223
|
-0.282
|
| HMC_vs_DEMetro_Z |
2
|
-0.930
|
0.364
|
-0.208
|
| HMC_vs_DEMetro_Z |
3
|
-1.104
|
0.284
|
-0.247
|
| HMC_vs_DEMetro_Z |
4
|
-2.011
|
0.0588
|
-0.450
|
| HMC_vs_DEMetro_Z |
5
|
-0.768
|
0.452
|
-0.172
|
| HMC_vs_Metro |
0
|
1.888
|
0.0744
|
0.422
|
| HMC_vs_Metro |
1
|
-0.523
|
0.607
|
-0.117
|
| HMC_vs_Metro |
2
|
-1.769
|
0.093
|
-0.395
|
| HMC_vs_Metro |
3
|
-0.424
|
0.676
|
-0.095
|
| HMC_vs_Metro |
4
|
-0.029
|
0.977
|
-0.007
|
| HMC_vs_Metro |
5
|
-0.205
|
0.84
|
-0.046
|
| HMC_vs_SMC |
0
|
5.117
|
6.12e-05
|
1.144
|
| HMC_vs_SMC |
1
|
4.101
|
0.000609
|
0.917
|
| HMC_vs_SMC |
2
|
3.602
|
0.0019
|
0.805
|
| HMC_vs_SMC |
3
|
4.392
|
0.000313
|
0.982
|
| HMC_vs_SMC |
4
|
4.923
|
9.45e-05
|
1.101
|
| HMC_vs_SMC |
5
|
6.056
|
7.98e-06
|
1.354
|
| Metro_vs_SMC |
0
|
7.408
|
5.15e-07
|
1.656
|
| Metro_vs_SMC |
1
|
5.685
|
1.76e-05
|
1.271
|
| Metro_vs_SMC |
2
|
4.363
|
0.000335
|
0.976
|
| Metro_vs_SMC |
3
|
5.554
|
2.34e-05
|
1.242
|
| Metro_vs_SMC |
4
|
4.779
|
0.00013
|
1.069
|
| Metro_vs_SMC |
5
|
7.122
|
9.01e-07
|
1.592
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.692 |
0.049 |
0.016 |
39.879 |
| HMC |
8 |
0.831 |
0.058 |
0.025 |
31.457 |
| HMC |
10 |
0.840 |
0.063 |
0.039 |
20.024 |
| HMC |
12 |
1.134 |
0.095 |
0.057 |
18.108 |
| HMC |
15 |
1.904 |
0.084 |
0.038 |
48.006 |
| HMC |
18 |
2.767 |
0.133 |
0.084 |
31.268 |
| SMC |
5 |
0.047 |
0.049 |
0.016 |
-0.129 |
| SMC |
8 |
0.076 |
0.058 |
0.025 |
0.709 |
| SMC |
10 |
0.070 |
0.063 |
0.039 |
0.162 |
| SMC |
12 |
0.092 |
0.095 |
0.057 |
-0.048 |
| SMC |
15 |
0.114 |
0.084 |
0.038 |
0.798 |
| SMC |
18 |
0.142 |
0.133 |
0.084 |
0.105 |
| Metro |
5 |
0.476 |
0.049 |
0.016 |
26.519 |
| Metro |
8 |
0.942 |
0.058 |
0.025 |
35.985 |
| Metro |
10 |
1.277 |
0.063 |
0.039 |
31.281 |
| Metro |
12 |
1.248 |
0.095 |
0.057 |
20.088 |
| Metro |
15 |
1.916 |
0.084 |
0.038 |
48.320 |
| Metro |
18 |
2.848 |
0.133 |
0.084 |
32.232 |
| DEMetro_Z |
5 |
0.559 |
0.049 |
0.016 |
31.648 |
| DEMetro_Z |
8 |
1.121 |
0.058 |
0.025 |
43.266 |
| DEMetro_Z |
10 |
1.081 |
0.063 |
0.039 |
26.226 |
| DEMetro_Z |
12 |
1.526 |
0.095 |
0.057 |
24.933 |
| DEMetro_Z |
15 |
2.981 |
0.084 |
0.038 |
76.398 |
| DEMetro_Z |
18 |
3.247 |
0.133 |
0.084 |
36.963 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.041 |
7.23e-05 |
43.654 |
| HMC |
8 |
4.230 |
0.000452 |
32.861 |
| HMC |
10 |
3.712 |
0.00147 |
21.424 |
| HMC |
12 |
4.479 |
0.000254 |
20.116 |
| HMC |
15 |
5.215 |
4.91e-05 |
45.586 |
| HMC |
18 |
6.277 |
4.95e-06 |
36.487 |
| SMC |
5 |
-0.384 |
0.703 |
-0.137 |
| SMC |
8 |
1.575 |
0.124 |
0.585 |
| SMC |
10 |
0.786 |
0.437 |
0.229 |
| SMC |
12 |
-0.152 |
0.88 |
-0.044 |
| SMC |
15 |
1.362 |
0.183 |
0.622 |
| SMC |
18 |
0.349 |
0.729 |
0.112 |
| Metro |
5 |
7.089 |
9.27e-07 |
27.735 |
| Metro |
8 |
5.614 |
2.04e-05 |
36.493 |
| Metro |
10 |
4.447 |
0.000276 |
32.741 |
| Metro |
12 |
5.404 |
3.18e-05 |
20.463 |
| Metro |
15 |
4.854 |
0.00011 |
43.570 |
| Metro |
18 |
7.177 |
7.93e-07 |
39.377 |
| DEMetro_Z |
5 |
5.591 |
2.14e-05 |
34.298 |
| DEMetro_Z |
8 |
7.688 |
2.95e-07 |
45.296 |
| DEMetro_Z |
10 |
5.332 |
3.77e-05 |
28.633 |
| DEMetro_Z |
12 |
5.174 |
5.34e-05 |
26.789 |
| DEMetro_Z |
15 |
8.121 |
1.33e-07 |
68.385 |
| DEMetro_Z |
18 |
9.360 |
1.45e-08 |
43.251 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
5.679
|
1.79e-05
|
1.270
|
| DEMetro_Z_vs_SMC |
1
|
7.598
|
3.57e-07
|
1.699
|
| DEMetro_Z_vs_SMC |
2
|
5.315
|
3.95e-05
|
1.188
|
| DEMetro_Z_vs_SMC |
3
|
5.191
|
5.19e-05
|
1.161
|
| DEMetro_Z_vs_SMC |
4
|
7.898
|
2.03e-07
|
1.766
|
| DEMetro_Z_vs_SMC |
5
|
9.181
|
2.05e-08
|
2.053
|
| HMC_vs_Metro |
0
|
2.145
|
0.0451
|
0.480
|
| HMC_vs_Metro |
1
|
-0.427
|
0.674
|
-0.095
|
| HMC_vs_Metro |
2
|
-1.660
|
0.113
|
-0.371
|
| HMC_vs_Metro |
3
|
-0.070
|
0.945
|
-0.016
|
| HMC_vs_Metro |
4
|
0.216
|
0.832
|
0.048
|
| HMC_vs_Metro |
5
|
-0.564
|
0.579
|
-0.126
|
| Metro_vs_DEMetro_Z |
0
|
-0.993
|
0.333
|
-0.222
|
| Metro_vs_DEMetro_Z |
1
|
-1.227
|
0.235
|
-0.274
|
| Metro_vs_DEMetro_Z |
2
|
0.483
|
0.634
|
0.108
|
| Metro_vs_DEMetro_Z |
3
|
-1.001
|
0.329
|
-0.224
|
| Metro_vs_DEMetro_Z |
4
|
-2.109
|
0.0485
|
-0.472
|
| Metro_vs_DEMetro_Z |
5
|
-0.541
|
0.595
|
-0.121
|
| HMC_vs_SMC |
0
|
5.059
|
6.96e-05
|
1.131
|
| HMC_vs_SMC |
1
|
4.212
|
0.000472
|
0.942
|
| HMC_vs_SMC |
2
|
3.690
|
0.00156
|
0.825
|
| HMC_vs_SMC |
3
|
4.529
|
0.00023
|
1.013
|
| HMC_vs_SMC |
4
|
5.091
|
6.49e-05
|
1.138
|
| HMC_vs_SMC |
5
|
6.384
|
4.01e-06
|
1.428
|
| Metro_vs_SMC |
0
|
7.005
|
1.14e-06
|
1.566
|
| Metro_vs_SMC |
1
|
5.546
|
2.39e-05
|
1.240
|
| Metro_vs_SMC |
2
|
4.407
|
0.000303
|
0.985
|
| Metro_vs_SMC |
3
|
5.414
|
3.18e-05
|
1.211
|
| Metro_vs_SMC |
4
|
4.755
|
0.000138
|
1.063
|
| Metro_vs_SMC |
5
|
7.184
|
7.97e-07
|
1.606
|
| HMC_vs_DEMetro_Z |
0
|
0.839
|
0.412
|
0.188
|
| HMC_vs_DEMetro_Z |
1
|
-1.331
|
0.199
|
-0.298
|
| HMC_vs_DEMetro_Z |
2
|
-1.009
|
0.326
|
-0.226
|
| HMC_vs_DEMetro_Z |
3
|
-0.978
|
0.34
|
-0.219
|
| HMC_vs_DEMetro_Z |
4
|
-1.850
|
0.08
|
-0.414
|
| HMC_vs_DEMetro_Z |
5
|
-0.822
|
0.421
|
-0.184
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.231 |
0.012 |
0.005 |
43.654 |
| HMC |
8 |
0.205 |
0.010 |
0.006 |
32.861 |
| HMC |
10 |
0.165 |
0.009 |
0.007 |
21.424 |
| HMC |
12 |
0.202 |
0.013 |
0.009 |
20.116 |
| HMC |
15 |
0.264 |
0.008 |
0.006 |
45.586 |
| HMC |
18 |
0.309 |
0.012 |
0.008 |
36.487 |
| SMC |
5 |
0.012 |
0.012 |
0.005 |
-0.137 |
| SMC |
8 |
0.014 |
0.010 |
0.006 |
0.585 |
| SMC |
10 |
0.010 |
0.009 |
0.007 |
0.229 |
| SMC |
12 |
0.012 |
0.013 |
0.009 |
-0.044 |
| SMC |
15 |
0.012 |
0.008 |
0.006 |
0.622 |
| SMC |
18 |
0.012 |
0.012 |
0.008 |
0.112 |
| Metro |
5 |
0.151 |
0.012 |
0.005 |
27.735 |
| Metro |
8 |
0.226 |
0.010 |
0.006 |
36.493 |
| Metro |
10 |
0.247 |
0.009 |
0.007 |
32.741 |
| Metro |
12 |
0.205 |
0.013 |
0.009 |
20.463 |
| Metro |
15 |
0.253 |
0.008 |
0.006 |
43.570 |
| Metro |
18 |
0.333 |
0.012 |
0.008 |
39.377 |
| DEMetro_Z |
5 |
0.184 |
0.012 |
0.005 |
34.298 |
| DEMetro_Z |
8 |
0.278 |
0.010 |
0.006 |
45.296 |
| DEMetro_Z |
10 |
0.217 |
0.009 |
0.007 |
28.633 |
| DEMetro_Z |
12 |
0.264 |
0.013 |
0.009 |
26.789 |
| DEMetro_Z |
15 |
0.392 |
0.008 |
0.006 |
68.385 |
| DEMetro_Z |
18 |
0.364 |
0.012 |
0.008 |
43.251 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
178.260 |
1.25e-43 |
91.337 |
| HMC |
8 |
210.921 |
5.18e-54 |
83.569 |
| HMC |
10 |
205.637 |
2.17e-57 |
73.168 |
| HMC |
12 |
194.815 |
2.7e-58 |
59.248 |
| HMC |
15 |
226.819 |
1.26e-48 |
107.934 |
| HMC |
18 |
236.657 |
1.04e-55 |
64.118 |
| SMC |
5 |
0.102 |
0.92 |
0.040 |
| SMC |
8 |
1.318 |
0.196 |
0.451 |
| SMC |
10 |
1.914 |
0.0632 |
0.619 |
| SMC |
12 |
-0.395 |
0.695 |
-0.114 |
| SMC |
15 |
1.474 |
0.151 |
0.683 |
| SMC |
18 |
-1.340 |
0.189 |
-0.371 |
| Metro |
5 |
5.619 |
2.02e-05 |
34.774 |
| Metro |
8 |
149.220 |
1.27e-39 |
83.532 |
| Metro |
10 |
197.561 |
1.95e-55 |
73.218 |
| Metro |
12 |
162.410 |
5.1e-53 |
59.068 |
| Metro |
15 |
177.659 |
3.77e-40 |
107.276 |
| Metro |
18 |
218.978 |
2.7e-59 |
64.339 |
| DEMetro_Z |
5 |
6.965 |
1.22e-06 |
64.809 |
| DEMetro_Z |
8 |
21.213 |
9.34e-15 |
79.867 |
| DEMetro_Z |
10 |
199.277 |
1.13e-55 |
73.628 |
| DEMetro_Z |
12 |
184.949 |
1.04e-57 |
59.437 |
| DEMetro_Z |
15 |
213.374 |
4.43e-46 |
108.064 |
| DEMetro_Z |
18 |
230.810 |
2.09e-57 |
64.299 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
2.783
|
0.0119
|
0.622
|
| HMC_vs_DEMetro_Z |
1
|
0.962
|
0.348
|
0.215
|
| HMC_vs_DEMetro_Z |
2
|
-1.501
|
0.15
|
-0.336
|
| HMC_vs_DEMetro_Z |
3
|
-0.715
|
0.483
|
-0.160
|
| HMC_vs_DEMetro_Z |
4
|
-0.190
|
0.851
|
-0.043
|
| HMC_vs_DEMetro_Z |
5
|
-0.894
|
0.383
|
-0.200
|
| Metro_vs_SMC |
0
|
5.612
|
2.07e-05
|
1.255
|
| Metro_vs_SMC |
1
|
138.837
|
4.94e-30
|
31.045
|
| Metro_vs_SMC |
2
|
181.660
|
3e-32
|
40.620
|
| Metro_vs_SMC |
3
|
173.223
|
7.4e-32
|
38.734
|
| Metro_vs_SMC |
4
|
122.341
|
5.45e-29
|
27.356
|
| Metro_vs_SMC |
5
|
223.756
|
5.73e-34
|
50.033
|
| Metro_vs_DEMetro_Z |
0
|
-2.282
|
0.0342
|
-0.510
|
| Metro_vs_DEMetro_Z |
1
|
0.964
|
0.347
|
0.216
|
| Metro_vs_DEMetro_Z |
2
|
-0.857
|
0.402
|
-0.192
|
| Metro_vs_DEMetro_Z |
3
|
-1.070
|
0.298
|
-0.239
|
| Metro_vs_DEMetro_Z |
4
|
-1.132
|
0.272
|
-0.253
|
| Metro_vs_DEMetro_Z |
5
|
0.171
|
0.866
|
0.038
|
| HMC_vs_Metro |
0
|
9.058
|
2.53e-08
|
2.025
|
| HMC_vs_Metro |
1
|
0.083
|
0.934
|
0.019
|
| HMC_vs_Metro |
2
|
-0.106
|
0.917
|
-0.024
|
| HMC_vs_Metro |
3
|
0.752
|
0.461
|
0.168
|
| HMC_vs_Metro |
4
|
1.549
|
0.138
|
0.346
|
| HMC_vs_Metro |
5
|
-1.966
|
0.0641
|
-0.440
|
| HMC_vs_SMC |
0
|
144.952
|
2.18e-30
|
32.412
|
| HMC_vs_SMC |
1
|
184.816
|
2.16e-32
|
41.326
|
| HMC_vs_SMC |
2
|
198.648
|
5.49e-33
|
44.419
|
| HMC_vs_SMC |
3
|
195.639
|
7.34e-33
|
43.746
|
| HMC_vs_SMC |
4
|
149.500
|
1.21e-30
|
33.429
|
| HMC_vs_SMC |
5
|
243.743
|
1.13e-34
|
54.503
|
| DEMetro_Z_vs_SMC |
0
|
6.926
|
1.33e-06
|
1.549
|
| DEMetro_Z_vs_SMC |
1
|
21.392
|
9.34e-15
|
4.783
|
| DEMetro_Z_vs_SMC |
2
|
307.755
|
1.34e-36
|
68.816
|
| DEMetro_Z_vs_SMC |
3
|
188.560
|
1.48e-32
|
42.163
|
| DEMetro_Z_vs_SMC |
4
|
170.632
|
9.85e-32
|
38.155
|
| DEMetro_Z_vs_SMC |
5
|
249.059
|
7.48e-35
|
55.691
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.765 |
0.034 |
0.019 |
91.337 |
| HMC |
8 |
2.832 |
0.047 |
0.033 |
83.569 |
| HMC |
10 |
3.536 |
0.048 |
0.048 |
73.168 |
| HMC |
12 |
4.255 |
0.088 |
0.070 |
59.248 |
| HMC |
15 |
5.280 |
0.073 |
0.048 |
107.934 |
| HMC |
18 |
6.361 |
0.135 |
0.097 |
64.118 |
| SMC |
5 |
0.035 |
0.034 |
0.019 |
0.040 |
| SMC |
8 |
0.062 |
0.047 |
0.033 |
0.451 |
| SMC |
10 |
0.078 |
0.048 |
0.048 |
0.619 |
| SMC |
12 |
0.080 |
0.088 |
0.070 |
-0.114 |
| SMC |
15 |
0.106 |
0.073 |
0.048 |
0.683 |
| SMC |
18 |
0.099 |
0.135 |
0.097 |
-0.371 |
| Metro |
5 |
0.693 |
0.034 |
0.019 |
34.774 |
| Metro |
8 |
2.831 |
0.047 |
0.033 |
83.532 |
| Metro |
10 |
3.538 |
0.048 |
0.048 |
73.218 |
| Metro |
12 |
4.243 |
0.088 |
0.070 |
59.068 |
| Metro |
15 |
5.248 |
0.073 |
0.048 |
107.276 |
| Metro |
18 |
6.382 |
0.135 |
0.097 |
64.339 |
| DEMetro_Z |
5 |
1.262 |
0.034 |
0.019 |
64.809 |
| DEMetro_Z |
8 |
2.709 |
0.047 |
0.033 |
79.867 |
| DEMetro_Z |
10 |
3.558 |
0.048 |
0.048 |
73.628 |
| DEMetro_Z |
12 |
4.269 |
0.088 |
0.070 |
59.437 |
| DEMetro_Z |
15 |
5.286 |
0.073 |
0.048 |
108.064 |
| DEMetro_Z |
18 |
6.378 |
0.135 |
0.097 |
64.299 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
207.553 |
8.5e-47 |
101.201 |
| HMC |
8 |
334.946 |
1.13e-58 |
139.403 |
| HMC |
10 |
536.571 |
4.36e-69 |
206.210 |
| HMC |
12 |
655.129 |
4.86e-68 |
272.803 |
| HMC |
15 |
739.594 |
6.69e-76 |
273.069 |
| HMC |
18 |
1020.837 |
2.43e-81 |
373.472 |
| SMC |
5 |
-0.299 |
0.766 |
-0.099 |
| SMC |
8 |
1.251 |
0.219 |
0.434 |
| SMC |
10 |
0.202 |
0.841 |
0.070 |
| SMC |
12 |
1.201 |
0.237 |
0.421 |
| SMC |
15 |
-1.083 |
0.288 |
-0.273 |
| SMC |
18 |
0.690 |
0.495 |
0.243 |
| Metro |
5 |
3.805 |
0.00119 |
25.706 |
| Metro |
8 |
363.515 |
2.32e-63 |
139.405 |
| Metro |
10 |
522.171 |
2.12e-67 |
206.141 |
| Metro |
12 |
550.654 |
2.93e-58 |
272.822 |
| Metro |
15 |
732.732 |
2.68e-75 |
273.078 |
| Metro |
18 |
957.046 |
7.27e-77 |
373.686 |
| DEMetro_Z |
5 |
6.657 |
2.28e-06 |
71.116 |
| DEMetro_Z |
8 |
19.581 |
4.48e-14 |
132.904 |
| DEMetro_Z |
10 |
577.690 |
1.25e-73 |
205.957 |
| DEMetro_Z |
12 |
638.499 |
1.95e-66 |
272.774 |
| DEMetro_Z |
15 |
718.064 |
5.72e-74 |
273.116 |
| DEMetro_Z |
18 |
1003.685 |
3.45e-80 |
373.520 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
238.979
|
1.64e-34
|
53.437
|
| HMC_vs_SMC |
1
|
278.204
|
9.14e-36
|
62.208
|
| HMC_vs_SMC |
2
|
702.257
|
2.1e-43
|
157.029
|
| HMC_vs_SMC |
3
|
566.820
|
1.23e-41
|
126.745
|
| HMC_vs_SMC |
4
|
834.229
|
7.95e-45
|
186.539
|
| HMC_vs_SMC |
5
|
809.861
|
1.4e-44
|
181.090
|
| Metro_vs_DEMetro_Z |
0
|
-2.972
|
0.00783
|
-0.665
|
| Metro_vs_DEMetro_Z |
1
|
0.956
|
0.351
|
0.214
|
| Metro_vs_DEMetro_Z |
2
|
0.875
|
0.392
|
0.196
|
| Metro_vs_DEMetro_Z |
3
|
0.230
|
0.82
|
0.051
|
| Metro_vs_DEMetro_Z |
4
|
-0.347
|
0.733
|
-0.077
|
| Metro_vs_DEMetro_Z |
5
|
1.351
|
0.193
|
0.302
|
| HMC_vs_Metro |
0
|
11.156
|
8.79e-10
|
2.495
|
| HMC_vs_Metro |
1
|
-0.008
|
0.994
|
-0.002
|
| HMC_vs_Metro |
2
|
0.313
|
0.758
|
0.070
|
| HMC_vs_Metro |
3
|
-0.103
|
0.919
|
-0.023
|
| HMC_vs_Metro |
4
|
-0.075
|
0.941
|
-0.017
|
| HMC_vs_Metro |
5
|
-2.295
|
0.0333
|
-0.513
|
| HMC_vs_DEMetro_Z |
0
|
2.812
|
0.0111
|
0.629
|
| HMC_vs_DEMetro_Z |
1
|
0.961
|
0.349
|
0.215
|
| HMC_vs_DEMetro_Z |
2
|
2.090
|
0.0503
|
0.467
|
| HMC_vs_DEMetro_Z |
3
|
0.217
|
0.83
|
0.049
|
| HMC_vs_DEMetro_Z |
4
|
-0.525
|
0.606
|
-0.117
|
| HMC_vs_DEMetro_Z |
5
|
-0.612
|
0.548
|
-0.137
|
| Metro_vs_SMC |
0
|
3.801
|
0.00121
|
0.850
|
| Metro_vs_SMC |
1
|
316.075
|
8.1e-37
|
70.676
|
| Metro_vs_SMC |
2
|
572.223
|
1.03e-41
|
127.953
|
| Metro_vs_SMC |
3
|
451.901
|
9.1e-40
|
101.048
|
| Metro_vs_SMC |
4
|
799.753
|
1.77e-44
|
178.830
|
| Metro_vs_SMC |
5
|
801.471
|
1.7e-44
|
179.214
|
| DEMetro_Z_vs_SMC |
0
|
6.695
|
2.12e-06
|
1.497
|
| DEMetro_Z_vs_SMC |
1
|
19.718
|
4.12e-14
|
4.409
|
| DEMetro_Z_vs_SMC |
2
|
691.958
|
2.78e-43
|
154.727
|
| DEMetro_Z_vs_SMC |
3
|
554.422
|
1.87e-41
|
123.972
|
| DEMetro_Z_vs_SMC |
4
|
820.678
|
1.09e-44
|
183.509
|
| DEMetro_Z_vs_SMC |
5
|
802.535
|
1.66e-44
|
179.452
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
4.426 |
0.077 |
0.043 |
101.201 |
| HMC |
8 |
11.304 |
0.089 |
0.080 |
139.403 |
| HMC |
10 |
17.706 |
0.120 |
0.085 |
206.210 |
| HMC |
12 |
25.437 |
0.141 |
0.093 |
272.803 |
| HMC |
15 |
39.767 |
0.205 |
0.145 |
273.069 |
| HMC |
18 |
57.255 |
0.184 |
0.153 |
373.472 |
| SMC |
5 |
0.073 |
0.077 |
0.043 |
-0.099 |
| SMC |
8 |
0.124 |
0.089 |
0.080 |
0.434 |
| SMC |
10 |
0.126 |
0.120 |
0.085 |
0.070 |
| SMC |
12 |
0.180 |
0.141 |
0.093 |
0.421 |
| SMC |
15 |
0.165 |
0.205 |
0.145 |
-0.273 |
| SMC |
18 |
0.221 |
0.184 |
0.153 |
0.243 |
| Metro |
5 |
1.182 |
0.077 |
0.043 |
25.706 |
| Metro |
8 |
11.304 |
0.089 |
0.080 |
139.405 |
| Metro |
10 |
17.700 |
0.120 |
0.085 |
206.141 |
| Metro |
12 |
25.439 |
0.141 |
0.093 |
272.822 |
| Metro |
15 |
39.768 |
0.205 |
0.145 |
273.078 |
| Metro |
18 |
57.288 |
0.184 |
0.153 |
373.686 |
| DEMetro_Z |
5 |
3.133 |
0.077 |
0.043 |
71.116 |
| DEMetro_Z |
8 |
10.781 |
0.089 |
0.080 |
132.904 |
| DEMetro_Z |
10 |
17.684 |
0.120 |
0.085 |
205.957 |
| DEMetro_Z |
12 |
25.435 |
0.141 |
0.093 |
272.774 |
| DEMetro_Z |
15 |
39.774 |
0.205 |
0.145 |
273.116 |
| DEMetro_Z |
18 |
57.262 |
0.184 |
0.153 |
373.520 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
73.984 |
5.11e-26 |
96.576 |
| HMC |
8 |
62.169 |
4.08e-24 |
100.794 |
| HMC |
10 |
65.878 |
2.99e-25 |
78.048 |
| HMC |
12 |
62.523 |
3.76e-25 |
65.851 |
| HMC |
15 |
74.145 |
1.44e-25 |
124.496 |
| HMC |
18 |
72.843 |
2.85e-27 |
64.936 |
| SMC |
5 |
-0.335 |
0.74 |
-0.120 |
| SMC |
8 |
1.628 |
0.113 |
0.629 |
| SMC |
10 |
1.892 |
0.0662 |
0.589 |
| SMC |
12 |
-0.386 |
0.701 |
-0.110 |
| SMC |
15 |
1.346 |
0.189 |
0.655 |
| SMC |
18 |
-1.177 |
0.247 |
-0.322 |
| Metro |
5 |
5.770 |
1.45e-05 |
36.998 |
| Metro |
8 |
58.362 |
1.75e-23 |
101.736 |
| Metro |
10 |
54.459 |
4.15e-23 |
81.189 |
| Metro |
12 |
63.163 |
3.01e-25 |
66.437 |
| Metro |
15 |
77.969 |
3.98e-26 |
120.549 |
| Metro |
18 |
80.222 |
1.7e-28 |
67.660 |
| DEMetro_Z |
5 |
6.918 |
1.34e-06 |
68.636 |
| DEMetro_Z |
8 |
19.157 |
6.44e-14 |
97.835 |
| DEMetro_Z |
10 |
74.148 |
1.45e-26 |
80.746 |
| DEMetro_Z |
12 |
59.762 |
1.48e-24 |
66.804 |
| DEMetro_Z |
15 |
58.874 |
2.3e-23 |
125.255 |
| DEMetro_Z |
18 |
72.686 |
3.49e-27 |
65.641 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.310
|
0.0323
|
-0.517
|
| Metro_vs_DEMetro_Z |
1
|
0.691
|
0.498
|
0.155
|
| Metro_vs_DEMetro_Z |
2
|
0.220
|
0.828
|
0.049
|
| Metro_vs_DEMetro_Z |
3
|
-0.238
|
0.814
|
-0.053
|
| Metro_vs_DEMetro_Z |
4
|
-1.688
|
0.108
|
-0.377
|
| Metro_vs_DEMetro_Z |
5
|
2.311
|
0.0322
|
0.517
|
| DEMetro_Z_vs_SMC |
0
|
6.903
|
1.39e-06
|
1.544
|
| DEMetro_Z_vs_SMC |
1
|
19.337
|
5.87e-14
|
4.324
|
| DEMetro_Z_vs_SMC |
2
|
81.144
|
1.31e-25
|
18.144
|
| DEMetro_Z_vs_SMC |
3
|
60.199
|
3.74e-23
|
13.461
|
| DEMetro_Z_vs_SMC |
4
|
56.410
|
1.28e-22
|
12.614
|
| DEMetro_Z_vs_SMC |
5
|
71.027
|
1.63e-24
|
15.882
|
| HMC_vs_DEMetro_Z |
0
|
2.711
|
0.0139
|
0.606
|
| HMC_vs_DEMetro_Z |
1
|
0.523
|
0.607
|
0.117
|
| HMC_vs_DEMetro_Z |
2
|
-1.409
|
0.175
|
-0.315
|
| HMC_vs_DEMetro_Z |
3
|
-0.683
|
0.503
|
-0.153
|
| HMC_vs_DEMetro_Z |
4
|
-0.261
|
0.797
|
-0.058
|
| HMC_vs_DEMetro_Z |
5
|
-0.534
|
0.599
|
-0.119
|
| HMC_vs_Metro |
0
|
9.130
|
2.23e-08
|
2.042
|
| HMC_vs_Metro |
1
|
-0.357
|
0.725
|
-0.080
|
| HMC_vs_Metro |
2
|
-1.829
|
0.0831
|
-0.409
|
| HMC_vs_Metro |
3
|
-0.408
|
0.688
|
-0.091
|
| HMC_vs_Metro |
4
|
1.492
|
0.152
|
0.334
|
| HMC_vs_Metro |
5
|
-2.258
|
0.0359
|
-0.505
|
| HMC_vs_SMC |
0
|
73.184
|
9.27e-25
|
16.365
|
| HMC_vs_SMC |
1
|
62.535
|
1.82e-23
|
13.983
|
| HMC_vs_SMC |
2
|
61.458
|
2.52e-23
|
13.743
|
| HMC_vs_SMC |
3
|
63.424
|
1.39e-23
|
14.182
|
| HMC_vs_SMC |
4
|
67.882
|
3.85e-24
|
15.179
|
| HMC_vs_SMC |
5
|
72.018
|
1.26e-24
|
16.104
|
| Metro_vs_SMC |
0
|
5.781
|
1.43e-05
|
1.293
|
| Metro_vs_SMC |
1
|
58.932
|
5.58e-23
|
13.178
|
| Metro_vs_SMC |
2
|
52.641
|
4.71e-22
|
11.771
|
| Metro_vs_SMC |
3
|
62.281
|
1.96e-23
|
13.926
|
| Metro_vs_SMC |
4
|
71.069
|
1.62e-24
|
15.891
|
| Metro_vs_SMC |
5
|
84.899
|
5.57e-26
|
18.984
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.605 |
0.049 |
0.016 |
96.576 |
| HMC |
8 |
2.533 |
0.058 |
0.025 |
100.794 |
| HMC |
10 |
3.091 |
0.063 |
0.039 |
78.048 |
| HMC |
12 |
3.874 |
0.095 |
0.057 |
65.851 |
| HMC |
15 |
4.806 |
0.084 |
0.038 |
124.496 |
| HMC |
18 |
5.604 |
0.133 |
0.084 |
64.936 |
| SMC |
5 |
0.047 |
0.049 |
0.016 |
-0.120 |
| SMC |
8 |
0.074 |
0.058 |
0.025 |
0.629 |
| SMC |
10 |
0.086 |
0.063 |
0.039 |
0.589 |
| SMC |
12 |
0.088 |
0.095 |
0.057 |
-0.110 |
| SMC |
15 |
0.108 |
0.084 |
0.038 |
0.655 |
| SMC |
18 |
0.106 |
0.133 |
0.084 |
-0.322 |
| Metro |
5 |
0.645 |
0.049 |
0.016 |
36.998 |
| Metro |
8 |
2.556 |
0.058 |
0.025 |
101.736 |
| Metro |
10 |
3.213 |
0.063 |
0.039 |
81.189 |
| Metro |
12 |
3.908 |
0.095 |
0.057 |
66.437 |
| Metro |
15 |
4.656 |
0.084 |
0.038 |
120.549 |
| Metro |
18 |
5.833 |
0.133 |
0.084 |
67.660 |
| DEMetro_Z |
5 |
1.155 |
0.049 |
0.016 |
68.636 |
| DEMetro_Z |
8 |
2.460 |
0.058 |
0.025 |
97.835 |
| DEMetro_Z |
10 |
3.196 |
0.063 |
0.039 |
80.746 |
| DEMetro_Z |
12 |
3.929 |
0.095 |
0.057 |
66.804 |
| DEMetro_Z |
15 |
4.834 |
0.084 |
0.038 |
125.255 |
| DEMetro_Z |
18 |
5.663 |
0.133 |
0.084 |
65.641 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
119.334 |
9.07e-32 |
108.219 |
| HMC |
8 |
165.929 |
6.66e-39 |
103.337 |
| HMC |
10 |
112.486 |
1.41e-32 |
85.066 |
| HMC |
12 |
154.479 |
1.54e-47 |
64.903 |
| HMC |
15 |
109.562 |
1.89e-30 |
109.348 |
| HMC |
18 |
129.571 |
1.8e-37 |
74.844 |
| SMC |
5 |
-0.140 |
0.889 |
-0.055 |
| SMC |
8 |
1.338 |
0.189 |
0.461 |
| SMC |
10 |
2.043 |
0.0481 |
0.669 |
| SMC |
12 |
-0.697 |
0.49 |
-0.194 |
| SMC |
15 |
1.332 |
0.192 |
0.573 |
| SMC |
18 |
-1.402 |
0.17 |
-0.386 |
| Metro |
5 |
5.470 |
2.8e-05 |
40.092 |
| Metro |
8 |
145.871 |
5.45e-36 |
101.870 |
| Metro |
10 |
154.546 |
1.93e-40 |
84.705 |
| Metro |
12 |
110.245 |
2.13e-35 |
64.841 |
| Metro |
15 |
138.105 |
3.23e-34 |
108.676 |
| Metro |
18 |
142.851 |
2.38e-40 |
75.318 |
| DEMetro_Z |
5 |
6.904 |
1.38e-06 |
76.950 |
| DEMetro_Z |
8 |
20.875 |
1.33e-14 |
98.487 |
| DEMetro_Z |
10 |
152.767 |
5.93e-40 |
85.224 |
| DEMetro_Z |
12 |
141.822 |
1.08e-43 |
65.125 |
| DEMetro_Z |
15 |
109.744 |
1.63e-30 |
108.481 |
| DEMetro_Z |
18 |
115.462 |
2.34e-34 |
75.765 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
6.883
|
1.45e-06
|
1.539
|
| DEMetro_Z_vs_SMC |
1
|
21.052
|
1.25e-14
|
4.707
|
| DEMetro_Z_vs_SMC |
2
|
172.971
|
7.6e-32
|
38.677
|
| DEMetro_Z_vs_SMC |
3
|
158.547
|
3.97e-31
|
35.452
|
| DEMetro_Z_vs_SMC |
4
|
107.920
|
5.88e-28
|
24.132
|
| DEMetro_Z_vs_SMC |
5
|
119.693
|
8.25e-29
|
26.764
|
| HMC_vs_Metro |
0
|
9.338
|
1.57e-08
|
2.088
|
| HMC_vs_Metro |
1
|
2.116
|
0.0477
|
0.473
|
| HMC_vs_Metro |
2
|
0.466
|
0.646
|
0.104
|
| HMC_vs_Metro |
3
|
0.087
|
0.931
|
0.020
|
| HMC_vs_Metro |
4
|
0.620
|
0.543
|
0.139
|
| HMC_vs_Metro |
5
|
-0.785
|
0.442
|
-0.176
|
| Metro_vs_DEMetro_Z |
0
|
-2.320
|
0.0316
|
-0.519
|
| Metro_vs_DEMetro_Z |
1
|
0.707
|
0.488
|
0.158
|
| Metro_vs_DEMetro_Z |
2
|
-0.699
|
0.493
|
-0.156
|
| Metro_vs_DEMetro_Z |
3
|
-0.458
|
0.652
|
-0.102
|
| Metro_vs_DEMetro_Z |
4
|
0.161
|
0.874
|
0.036
|
| Metro_vs_DEMetro_Z |
5
|
-0.526
|
0.605
|
-0.118
|
| HMC_vs_SMC |
0
|
105.612
|
8.87e-28
|
23.616
|
| HMC_vs_SMC |
1
|
148.008
|
1.47e-30
|
33.096
|
| HMC_vs_SMC |
2
|
122.403
|
5.39e-29
|
27.370
|
| HMC_vs_SMC |
3
|
155.707
|
5.6e-31
|
34.817
|
| HMC_vs_SMC |
4
|
89.965
|
1.86e-26
|
20.117
|
| HMC_vs_SMC |
5
|
137.896
|
5.62e-30
|
30.835
|
| Metro_vs_SMC |
0
|
5.478
|
2.76e-05
|
1.225
|
| Metro_vs_SMC |
1
|
131.366
|
1.41e-29
|
29.374
|
| Metro_vs_SMC |
2
|
151.952
|
8.9e-31
|
33.978
|
| Metro_vs_SMC |
3
|
123.185
|
4.78e-29
|
27.545
|
| Metro_vs_SMC |
4
|
130.288
|
1.65e-29
|
29.133
|
| Metro_vs_SMC |
5
|
136.351
|
6.96e-30
|
30.489
|
| HMC_vs_DEMetro_Z |
0
|
2.725
|
0.0135
|
0.609
|
| HMC_vs_DEMetro_Z |
1
|
0.974
|
0.342
|
0.218
|
| HMC_vs_DEMetro_Z |
2
|
-0.204
|
0.841
|
-0.046
|
| HMC_vs_DEMetro_Z |
3
|
-0.348
|
0.732
|
-0.078
|
| HMC_vs_DEMetro_Z |
4
|
0.629
|
0.537
|
0.141
|
| HMC_vs_DEMetro_Z |
5
|
-0.939
|
0.36
|
-0.210
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.553 |
0.012 |
0.005 |
108.219 |
| HMC |
8 |
0.622 |
0.010 |
0.006 |
103.337 |
| HMC |
10 |
0.628 |
0.009 |
0.007 |
85.066 |
| HMC |
12 |
0.622 |
0.013 |
0.009 |
64.903 |
| HMC |
15 |
0.622 |
0.008 |
0.006 |
109.348 |
| HMC |
18 |
0.622 |
0.012 |
0.008 |
74.844 |
| SMC |
5 |
0.012 |
0.012 |
0.005 |
-0.055 |
| SMC |
8 |
0.013 |
0.010 |
0.006 |
0.461 |
| SMC |
10 |
0.013 |
0.009 |
0.007 |
0.669 |
| SMC |
12 |
0.011 |
0.013 |
0.009 |
-0.194 |
| SMC |
15 |
0.012 |
0.008 |
0.006 |
0.573 |
| SMC |
18 |
0.008 |
0.012 |
0.008 |
-0.386 |
| Metro |
5 |
0.213 |
0.012 |
0.005 |
40.092 |
| Metro |
8 |
0.613 |
0.010 |
0.006 |
101.870 |
| Metro |
10 |
0.625 |
0.009 |
0.007 |
84.705 |
| Metro |
12 |
0.622 |
0.013 |
0.009 |
64.841 |
| Metro |
15 |
0.619 |
0.008 |
0.006 |
108.676 |
| Metro |
18 |
0.626 |
0.012 |
0.008 |
75.318 |
| DEMetro_Z |
5 |
0.397 |
0.012 |
0.005 |
76.950 |
| DEMetro_Z |
8 |
0.593 |
0.010 |
0.006 |
98.487 |
| DEMetro_Z |
10 |
0.629 |
0.009 |
0.007 |
85.224 |
| DEMetro_Z |
12 |
0.624 |
0.013 |
0.009 |
65.125 |
| DEMetro_Z |
15 |
0.618 |
0.008 |
0.006 |
108.481 |
| DEMetro_Z |
18 |
0.630 |
0.012 |
0.008 |
75.765 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_heavy_Tails
(Mixture,
mm,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.500 |
0.0178 |
1.062 |
| HMC |
8 |
3.527 |
0.00171 |
2.265 |
| HMC |
10 |
4.894 |
3.49e-05 |
2.355 |
| HMC |
12 |
4.954 |
6.12e-05 |
4.299 |
| HMC |
15 |
5.853 |
1.12e-05 |
12.435 |
| HMC |
18 |
4.641 |
0.000158 |
6.562 |
| SMC |
5 |
3.169 |
0.0038 |
1.679 |
| SMC |
8 |
3.865 |
0.000732 |
2.466 |
| SMC |
10 |
3.603 |
0.00129 |
1.990 |
| SMC |
12 |
4.095 |
0.000462 |
3.153 |
| SMC |
15 |
4.736 |
0.000125 |
6.293 |
| SMC |
18 |
4.884 |
8.89e-05 |
6.593 |
| Metro |
5 |
3.175 |
0.00461 |
3.387 |
| Metro |
8 |
3.518 |
0.00147 |
1.697 |
| Metro |
10 |
3.861 |
0.000441 |
1.349 |
| Metro |
12 |
3.299 |
0.0032 |
2.527 |
| Metro |
15 |
3.753 |
0.00116 |
3.650 |
| Metro |
18 |
5.101 |
2.64e-05 |
2.891 |
| DEMetro_Z |
5 |
4.665 |
8.74e-05 |
2.758 |
| DEMetro_Z |
8 |
6.432 |
2.58e-06 |
7.616 |
| DEMetro_Z |
10 |
4.766 |
4.78e-05 |
2.244 |
| DEMetro_Z |
12 |
7.619 |
2.49e-07 |
10.898 |
| DEMetro_Z |
15 |
4.941 |
8.85e-05 |
16.403 |
| DEMetro_Z |
18 |
5.876 |
1.1e-05 |
15.446 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.594
|
0.0178
|
-0.580
|
| HMC_vs_DEMetro_Z |
1
|
-3.570
|
0.00204
|
-0.798
|
| HMC_vs_DEMetro_Z |
2
|
0.172
|
0.865
|
0.038
|
| HMC_vs_DEMetro_Z |
3
|
-3.696
|
0.00154
|
-0.826
|
| HMC_vs_DEMetro_Z |
4
|
-0.960
|
0.349
|
-0.215
|
| HMC_vs_DEMetro_Z |
5
|
-2.976
|
0.00777
|
-0.665
|
| Metro_vs_SMC |
0
|
1.372
|
0.186
|
0.307
|
| Metro_vs_SMC |
1
|
-1.199
|
0.245
|
-0.268
|
| Metro_vs_SMC |
2
|
-1.299
|
0.21
|
-0.290
|
| Metro_vs_SMC |
3
|
-0.519
|
0.61
|
-0.116
|
| Metro_vs_SMC |
4
|
-1.630
|
0.12
|
-0.365
|
| Metro_vs_SMC |
5
|
-2.347
|
0.0299
|
-0.525
|
| Metro_vs_DEMetro_Z |
0
|
0.578
|
0.57
|
0.129
|
| Metro_vs_DEMetro_Z |
1
|
-5.544
|
2.4e-05
|
-1.240
|
| Metro_vs_DEMetro_Z |
2
|
-1.780
|
0.0911
|
-0.398
|
| Metro_vs_DEMetro_Z |
3
|
-6.346
|
4.34e-06
|
-1.419
|
| Metro_vs_DEMetro_Z |
4
|
-3.439
|
0.00275
|
-0.769
|
| Metro_vs_DEMetro_Z |
5
|
-5.147
|
5.74e-05
|
-1.151
|
| HMC_vs_Metro |
0
|
-1.928
|
0.0689
|
-0.431
|
| HMC_vs_Metro |
1
|
0.717
|
0.482
|
0.160
|
| HMC_vs_Metro |
2
|
2.370
|
0.0286
|
0.530
|
| HMC_vs_Metro |
3
|
1.697
|
0.106
|
0.379
|
| HMC_vs_Metro |
4
|
4.224
|
0.000459
|
0.945
|
| HMC_vs_Metro |
5
|
2.482
|
0.0226
|
0.555
|
| HMC_vs_SMC |
0
|
-0.999
|
0.331
|
-0.223
|
| HMC_vs_SMC |
1
|
-0.222
|
0.827
|
-0.050
|
| HMC_vs_SMC |
2
|
0.646
|
0.526
|
0.144
|
| HMC_vs_SMC |
3
|
1.059
|
0.303
|
0.237
|
| HMC_vs_SMC |
4
|
2.604
|
0.0175
|
0.582
|
| HMC_vs_SMC |
5
|
-0.014
|
0.989
|
-0.003
|
| DEMetro_Z_vs_SMC |
0
|
1.514
|
0.146
|
0.339
|
| DEMetro_Z_vs_SMC |
1
|
4.222
|
0.000461
|
0.944
|
| DEMetro_Z_vs_SMC |
2
|
0.380
|
0.708
|
0.085
|
| DEMetro_Z_vs_SMC |
3
|
4.358
|
0.000338
|
0.975
|
| DEMetro_Z_vs_SMC |
4
|
3.139
|
0.0054
|
0.702
|
| DEMetro_Z_vs_SMC |
5
|
2.952
|
0.00818
|
0.660
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.092 |
0.053 |
0.036 |
1.062 |
| HMC |
8 |
0.157 |
0.058 |
0.044 |
2.265 |
| HMC |
10 |
0.359 |
0.096 |
0.112 |
2.355 |
| HMC |
12 |
0.383 |
0.108 |
0.064 |
4.299 |
| HMC |
15 |
1.035 |
0.113 |
0.074 |
12.435 |
| HMC |
18 |
0.858 |
0.135 |
0.110 |
6.562 |
| SMC |
5 |
0.114 |
0.053 |
0.036 |
1.679 |
| SMC |
8 |
0.166 |
0.058 |
0.044 |
2.466 |
| SMC |
10 |
0.318 |
0.096 |
0.112 |
1.990 |
| SMC |
12 |
0.309 |
0.108 |
0.064 |
3.153 |
| SMC |
15 |
0.580 |
0.113 |
0.074 |
6.293 |
| SMC |
18 |
0.861 |
0.135 |
0.110 |
6.593 |
| Metro |
5 |
0.176 |
0.053 |
0.036 |
3.387 |
| Metro |
8 |
0.132 |
0.058 |
0.044 |
1.697 |
| Metro |
10 |
0.247 |
0.096 |
0.112 |
1.349 |
| Metro |
12 |
0.269 |
0.108 |
0.064 |
2.527 |
| Metro |
15 |
0.384 |
0.113 |
0.074 |
3.650 |
| Metro |
18 |
0.453 |
0.135 |
0.110 |
2.891 |
| DEMetro_Z |
5 |
0.153 |
0.053 |
0.036 |
2.758 |
| DEMetro_Z |
8 |
0.390 |
0.058 |
0.044 |
7.616 |
| DEMetro_Z |
10 |
0.347 |
0.096 |
0.112 |
2.244 |
| DEMetro_Z |
12 |
0.805 |
0.108 |
0.064 |
10.898 |
| DEMetro_Z |
15 |
1.330 |
0.113 |
0.074 |
16.403 |
| DEMetro_Z |
18 |
1.837 |
0.135 |
0.110 |
15.446 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
-1.505 |
0.149 |
-0.337 |
| HMC |
8 |
1.639 |
0.113 |
0.934 |
| HMC |
10 |
-0.792 |
0.437 |
-0.181 |
| HMC |
12 |
-1.230 |
0.232 |
-0.285 |
| HMC |
15 |
0.747 |
0.463 |
0.571 |
| HMC |
18 |
0.984 |
0.335 |
0.581 |
| SMC |
5 |
-1.434 |
0.168 |
-0.322 |
| SMC |
8 |
1.639 |
0.112 |
0.749 |
| SMC |
10 |
-0.768 |
0.451 |
-0.175 |
| SMC |
12 |
-1.516 |
0.146 |
-0.341 |
| SMC |
15 |
-1.087 |
0.29 |
-0.249 |
| SMC |
18 |
0.860 |
0.397 |
0.220 |
| Metro |
5 |
-1.119 |
0.275 |
-0.260 |
| Metro |
8 |
1.380 |
0.179 |
0.779 |
| Metro |
10 |
-0.776 |
0.447 |
-0.177 |
| Metro |
12 |
-1.428 |
0.169 |
-0.322 |
| Metro |
15 |
-0.878 |
0.388 |
-0.211 |
| Metro |
18 |
0.088 |
0.931 |
0.024 |
| DEMetro_Z |
5 |
-1.441 |
0.166 |
-0.323 |
| DEMetro_Z |
8 |
2.025 |
0.0531 |
1.101 |
| DEMetro_Z |
10 |
-0.788 |
0.44 |
-0.180 |
| DEMetro_Z |
12 |
-1.265 |
0.221 |
-0.285 |
| DEMetro_Z |
15 |
0.058 |
0.954 |
0.015 |
| DEMetro_Z |
18 |
2.548 |
0.0152 |
0.891 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-0.653
|
0.521
|
-0.146
|
| HMC_vs_SMC |
1
|
0.612
|
0.548
|
0.137
|
| HMC_vs_SMC |
2
|
-1.899
|
0.0728
|
-0.425
|
| HMC_vs_SMC |
3
|
0.924
|
0.367
|
0.207
|
| HMC_vs_SMC |
4
|
1.130
|
0.273
|
0.253
|
| HMC_vs_SMC |
5
|
0.727
|
0.476
|
0.163
|
| Metro_vs_DEMetro_Z |
0
|
0.949
|
0.355
|
0.212
|
| Metro_vs_DEMetro_Z |
1
|
-1.103
|
0.284
|
-0.247
|
| Metro_vs_DEMetro_Z |
2
|
0.745
|
0.466
|
0.167
|
| Metro_vs_DEMetro_Z |
3
|
-3.467
|
0.00258
|
-0.775
|
| Metro_vs_DEMetro_Z |
4
|
-1.937
|
0.0678
|
-0.433
|
| Metro_vs_DEMetro_Z |
5
|
-2.735
|
0.0132
|
-0.612
|
| HMC_vs_Metro |
0
|
-1.199
|
0.245
|
-0.268
|
| HMC_vs_Metro |
1
|
0.348
|
0.732
|
0.078
|
| HMC_vs_Metro |
2
|
-1.079
|
0.294
|
-0.241
|
| HMC_vs_Metro |
3
|
0.615
|
0.546
|
0.138
|
| HMC_vs_Metro |
4
|
1.056
|
0.304
|
0.236
|
| HMC_vs_Metro |
5
|
0.990
|
0.334
|
0.221
|
| HMC_vs_DEMetro_Z |
0
|
-1.593
|
0.128
|
-0.356
|
| HMC_vs_DEMetro_Z |
1
|
-0.445
|
0.662
|
-0.099
|
| HMC_vs_DEMetro_Z |
2
|
-0.736
|
0.471
|
-0.165
|
| HMC_vs_DEMetro_Z |
3
|
0.003
|
0.998
|
0.001
|
| HMC_vs_DEMetro_Z |
4
|
0.734
|
0.472
|
0.164
|
| HMC_vs_DEMetro_Z |
5
|
-0.529
|
0.603
|
-0.118
|
| Metro_vs_SMC |
0
|
0.917
|
0.37
|
0.205
|
| Metro_vs_SMC |
1
|
0.094
|
0.926
|
0.021
|
| Metro_vs_SMC |
2
|
-0.452
|
0.657
|
-0.101
|
| Metro_vs_SMC |
3
|
1.270
|
0.219
|
0.284
|
| Metro_vs_SMC |
4
|
0.467
|
0.646
|
0.104
|
| Metro_vs_SMC |
5
|
-1.111
|
0.28
|
-0.248
|
| DEMetro_Z_vs_SMC |
0
|
-0.058
|
0.955
|
-0.013
|
| DEMetro_Z_vs_SMC |
1
|
1.504
|
0.149
|
0.336
|
| DEMetro_Z_vs_SMC |
2
|
-1.592
|
0.128
|
-0.356
|
| DEMetro_Z_vs_SMC |
3
|
4.352
|
0.000343
|
0.973
|
| DEMetro_Z_vs_SMC |
4
|
2.295
|
0.0333
|
0.513
|
| DEMetro_Z_vs_SMC |
5
|
2.275
|
0.0346
|
0.509
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
3.673 |
17.284 |
40.350 |
-0.337 |
| HMC |
8 |
5.725 |
3.215 |
2.688 |
0.934 |
| HMC |
10 |
20.587 |
87.229 |
368.626 |
-0.181 |
| HMC |
12 |
6.550 |
19.100 |
44.067 |
-0.285 |
| HMC |
15 |
16.734 |
8.635 |
14.171 |
0.571 |
| HMC |
18 |
9.289 |
5.445 |
6.620 |
0.581 |
| SMC |
5 |
4.307 |
17.284 |
40.350 |
-0.322 |
| SMC |
8 |
5.228 |
3.215 |
2.688 |
0.749 |
| SMC |
10 |
22.668 |
87.229 |
368.626 |
-0.175 |
| SMC |
12 |
4.091 |
19.100 |
44.067 |
-0.341 |
| SMC |
15 |
5.110 |
8.635 |
14.171 |
-0.249 |
| SMC |
18 |
6.903 |
5.445 |
6.620 |
0.220 |
| Metro |
5 |
6.786 |
17.284 |
40.350 |
-0.260 |
| Metro |
8 |
5.308 |
3.215 |
2.688 |
0.779 |
| Metro |
10 |
21.972 |
87.229 |
368.626 |
-0.177 |
| Metro |
12 |
4.914 |
19.100 |
44.067 |
-0.322 |
| Metro |
15 |
5.642 |
8.635 |
14.171 |
-0.211 |
| Metro |
18 |
5.602 |
5.445 |
6.620 |
0.024 |
| DEMetro_Z |
5 |
4.247 |
17.284 |
40.350 |
-0.323 |
| DEMetro_Z |
8 |
6.175 |
3.215 |
2.688 |
1.101 |
| DEMetro_Z |
10 |
20.957 |
87.229 |
368.626 |
-0.180 |
| DEMetro_Z |
12 |
6.542 |
19.100 |
44.067 |
-0.285 |
| DEMetro_Z |
15 |
8.841 |
8.635 |
14.171 |
0.015 |
| DEMetro_Z |
18 |
11.341 |
5.445 |
6.620 |
0.891 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.518 |
0.0161 |
0.773 |
| HMC |
8 |
4.603 |
0.000127 |
3.380 |
| HMC |
10 |
4.868 |
3.2e-05 |
2.151 |
| HMC |
12 |
4.683 |
0.000117 |
4.041 |
| HMC |
15 |
5.888 |
1.06e-05 |
13.654 |
| HMC |
18 |
5.003 |
7.13e-05 |
8.316 |
| SMC |
5 |
5.223 |
2.19e-05 |
3.224 |
| SMC |
8 |
6.901 |
5.97e-07 |
5.529 |
| SMC |
10 |
7.921 |
8.75e-09 |
3.687 |
| SMC |
12 |
6.327 |
1.88e-06 |
4.581 |
| SMC |
15 |
6.173 |
4.92e-06 |
8.469 |
| SMC |
18 |
7.125 |
7.08e-07 |
11.223 |
| Metro |
5 |
3.774 |
0.000911 |
2.371 |
| Metro |
8 |
6.021 |
2.47e-06 |
3.442 |
| Metro |
10 |
4.949 |
1.62e-05 |
1.689 |
| Metro |
12 |
4.007 |
0.00053 |
2.692 |
| Metro |
15 |
4.133 |
0.000486 |
4.508 |
| Metro |
18 |
6.078 |
3e-06 |
4.096 |
| DEMetro_Z |
5 |
6.209 |
4.27e-07 |
2.365 |
| DEMetro_Z |
8 |
7.629 |
2.4e-07 |
10.566 |
| DEMetro_Z |
10 |
5.869 |
2.21e-06 |
2.757 |
| DEMetro_Z |
12 |
8.166 |
8.22e-08 |
10.946 |
| DEMetro_Z |
15 |
5.086 |
6.4e-05 |
17.001 |
| DEMetro_Z |
18 |
6.334 |
4.24e-06 |
19.842 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.010
|
0.992
|
0.002
|
| Metro_vs_DEMetro_Z |
1
|
-5.479
|
2.76e-05
|
-1.225
|
| Metro_vs_DEMetro_Z |
2
|
-2.280
|
0.0343
|
-0.510
|
| Metro_vs_DEMetro_Z |
3
|
-6.500
|
3.16e-06
|
-1.453
|
| Metro_vs_DEMetro_Z |
4
|
-3.289
|
0.00386
|
-0.735
|
| Metro_vs_DEMetro_Z |
5
|
-5.403
|
3.26e-05
|
-1.208
|
| DEMetro_Z_vs_SMC |
0
|
-1.189
|
0.249
|
-0.266
|
| DEMetro_Z_vs_SMC |
1
|
3.864
|
0.00104
|
0.864
|
| DEMetro_Z_vs_SMC |
2
|
-1.564
|
0.134
|
-0.350
|
| DEMetro_Z_vs_SMC |
3
|
3.786
|
0.00125
|
0.846
|
| DEMetro_Z_vs_SMC |
4
|
2.601
|
0.0176
|
0.582
|
| DEMetro_Z_vs_SMC |
5
|
2.452
|
0.0241
|
0.548
|
| HMC_vs_DEMetro_Z |
0
|
-4.394
|
0.000312
|
-0.983
|
| HMC_vs_DEMetro_Z |
1
|
-4.001
|
0.000765
|
-0.895
|
| HMC_vs_DEMetro_Z |
2
|
-1.075
|
0.296
|
-0.240
|
| HMC_vs_DEMetro_Z |
3
|
-4.191
|
0.000495
|
-0.937
|
| HMC_vs_DEMetro_Z |
4
|
-0.760
|
0.457
|
-0.170
|
| HMC_vs_DEMetro_Z |
5
|
-3.350
|
0.00337
|
-0.749
|
| HMC_vs_Metro |
0
|
-2.534
|
0.0202
|
-0.567
|
| HMC_vs_Metro |
1
|
-0.064
|
0.949
|
-0.014
|
| HMC_vs_Metro |
2
|
1.272
|
0.219
|
0.284
|
| HMC_vs_Metro |
3
|
1.362
|
0.189
|
0.304
|
| HMC_vs_Metro |
4
|
4.041
|
0.000698
|
0.904
|
| HMC_vs_Metro |
5
|
2.381
|
0.0279
|
0.532
|
| HMC_vs_SMC |
0
|
-4.617
|
0.000188
|
-1.032
|
| HMC_vs_SMC |
1
|
-1.923
|
0.0696
|
-0.430
|
| HMC_vs_SMC |
2
|
-3.537
|
0.0022
|
-0.791
|
| HMC_vs_SMC |
3
|
-0.491
|
0.629
|
-0.110
|
| HMC_vs_SMC |
4
|
2.033
|
0.0562
|
0.455
|
| HMC_vs_SMC |
5
|
-1.177
|
0.254
|
-0.263
|
| Metro_vs_SMC |
0
|
-0.921
|
0.368
|
-0.206
|
| Metro_vs_SMC |
1
|
-2.520
|
0.0208
|
-0.564
|
| Metro_vs_SMC |
2
|
-6.005
|
8.89e-06
|
-1.343
|
| Metro_vs_SMC |
3
|
-1.729
|
0.1
|
-0.387
|
| Metro_vs_SMC |
4
|
-2.278
|
0.0345
|
-0.509
|
| Metro_vs_SMC |
5
|
-3.848
|
0.00108
|
-0.861
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.179 |
0.135 |
0.057 |
0.773 |
| HMC |
8 |
0.247 |
0.133 |
0.034 |
3.380 |
| HMC |
10 |
0.412 |
0.171 |
0.112 |
2.151 |
| HMC |
12 |
0.435 |
0.191 |
0.060 |
4.041 |
| HMC |
15 |
1.067 |
0.176 |
0.065 |
13.654 |
| HMC |
18 |
0.865 |
0.213 |
0.078 |
8.316 |
| SMC |
5 |
0.319 |
0.135 |
0.057 |
3.224 |
| SMC |
8 |
0.319 |
0.133 |
0.034 |
5.529 |
| SMC |
10 |
0.585 |
0.171 |
0.112 |
3.687 |
| SMC |
12 |
0.468 |
0.191 |
0.060 |
4.581 |
| SMC |
15 |
0.729 |
0.176 |
0.065 |
8.469 |
| SMC |
18 |
1.092 |
0.213 |
0.078 |
11.223 |
| Metro |
5 |
0.270 |
0.135 |
0.057 |
2.371 |
| Metro |
8 |
0.249 |
0.133 |
0.034 |
3.442 |
| Metro |
10 |
0.361 |
0.171 |
0.112 |
1.689 |
| Metro |
12 |
0.353 |
0.191 |
0.060 |
2.692 |
| Metro |
15 |
0.470 |
0.176 |
0.065 |
4.508 |
| Metro |
18 |
0.534 |
0.213 |
0.078 |
4.096 |
| DEMetro_Z |
5 |
0.270 |
0.135 |
0.057 |
2.365 |
| DEMetro_Z |
8 |
0.489 |
0.133 |
0.034 |
10.566 |
| DEMetro_Z |
10 |
0.480 |
0.171 |
0.112 |
2.757 |
| DEMetro_Z |
12 |
0.853 |
0.191 |
0.060 |
10.946 |
| DEMetro_Z |
15 |
1.285 |
0.176 |
0.065 |
17.001 |
| DEMetro_Z |
18 |
1.768 |
0.213 |
0.078 |
19.842 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.584 |
8.95e-05 |
2.342 |
| HMC |
8 |
4.051 |
0.000531 |
3.315 |
| HMC |
10 |
5.609 |
1.81e-05 |
9.066 |
| HMC |
12 |
4.545 |
0.000194 |
5.994 |
| HMC |
15 |
5.584 |
2.09e-05 |
15.611 |
| HMC |
18 |
4.722 |
0.000137 |
8.339 |
| SMC |
5 |
5.861 |
8.63e-06 |
6.391 |
| SMC |
8 |
5.098 |
3.94e-05 |
3.948 |
| SMC |
10 |
6.414 |
3.09e-06 |
9.911 |
| SMC |
12 |
5.123 |
4.53e-05 |
5.217 |
| SMC |
15 |
5.241 |
4.06e-05 |
7.925 |
| SMC |
18 |
5.084 |
5.94e-05 |
8.544 |
| Metro |
5 |
4.947 |
3.91e-05 |
2.783 |
| Metro |
8 |
4.354 |
0.000159 |
2.137 |
| Metro |
10 |
6.221 |
2.5e-06 |
4.603 |
| Metro |
12 |
3.748 |
0.00118 |
3.731 |
| Metro |
15 |
3.593 |
0.00177 |
4.267 |
| Metro |
18 |
4.912 |
5.49e-05 |
3.354 |
| DEMetro_Z |
5 |
5.716 |
1.05e-05 |
5.217 |
| DEMetro_Z |
8 |
7.377 |
3.98e-07 |
10.306 |
| DEMetro_Z |
10 |
6.025 |
7.15e-06 |
9.391 |
| DEMetro_Z |
12 |
7.086 |
8.58e-07 |
15.468 |
| DEMetro_Z |
15 |
4.591 |
0.000197 |
20.757 |
| DEMetro_Z |
18 |
5.813 |
1.3e-05 |
21.832 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-0.771
|
0.45
|
-0.172
|
| DEMetro_Z_vs_SMC |
1
|
4.538
|
0.000225
|
1.015
|
| DEMetro_Z_vs_SMC |
2
|
-0.233
|
0.819
|
-0.052
|
| DEMetro_Z_vs_SMC |
3
|
3.920
|
0.00092
|
0.876
|
| DEMetro_Z_vs_SMC |
4
|
2.978
|
0.00773
|
0.666
|
| DEMetro_Z_vs_SMC |
5
|
3.188
|
0.00484
|
0.713
|
| HMC_vs_Metro |
0
|
-0.638
|
0.531
|
-0.143
|
| HMC_vs_Metro |
1
|
1.342
|
0.195
|
0.300
|
| HMC_vs_Metro |
2
|
2.613
|
0.0171
|
0.584
|
| HMC_vs_Metro |
3
|
1.463
|
0.16
|
0.327
|
| HMC_vs_Metro |
4
|
4.058
|
0.000671
|
0.907
|
| HMC_vs_Metro |
5
|
2.617
|
0.017
|
0.585
|
| Metro_vs_DEMetro_Z |
0
|
-2.265
|
0.0354
|
-0.507
|
| Metro_vs_DEMetro_Z |
1
|
-6.102
|
7.23e-06
|
-1.365
|
| Metro_vs_DEMetro_Z |
2
|
-2.953
|
0.00817
|
-0.660
|
| Metro_vs_DEMetro_Z |
3
|
-5.447
|
2.96e-05
|
-1.218
|
| Metro_vs_DEMetro_Z |
4
|
-3.327
|
0.00355
|
-0.744
|
| Metro_vs_DEMetro_Z |
5
|
-5.269
|
4.38e-05
|
-1.178
|
| HMC_vs_SMC |
0
|
-3.944
|
0.000871
|
-0.882
|
| HMC_vs_SMC |
1
|
-0.543
|
0.594
|
-0.121
|
| HMC_vs_SMC |
2
|
-0.444
|
0.662
|
-0.099
|
| HMC_vs_SMC |
3
|
0.496
|
0.626
|
0.111
|
| HMC_vs_SMC |
4
|
2.516
|
0.021
|
0.563
|
| HMC_vs_SMC |
5
|
-0.078
|
0.939
|
-0.017
|
| Metro_vs_SMC |
0
|
-2.899
|
0.00919
|
-0.648
|
| Metro_vs_SMC |
1
|
-2.536
|
0.0201
|
-0.567
|
| Metro_vs_SMC |
2
|
-3.126
|
0.00556
|
-0.699
|
| Metro_vs_SMC |
3
|
-0.933
|
0.363
|
-0.209
|
| Metro_vs_SMC |
4
|
-1.968
|
0.0638
|
-0.440
|
| Metro_vs_SMC |
5
|
-2.711
|
0.0139
|
-0.606
|
| HMC_vs_DEMetro_Z |
0
|
-2.887
|
0.00945
|
-0.646
|
| HMC_vs_DEMetro_Z |
1
|
-3.616
|
0.00184
|
-0.808
|
| HMC_vs_DEMetro_Z |
2
|
-0.134
|
0.895
|
-0.030
|
| HMC_vs_DEMetro_Z |
3
|
-3.448
|
0.0027
|
-0.771
|
| HMC_vs_DEMetro_Z |
4
|
-0.915
|
0.372
|
-0.205
|
| HMC_vs_DEMetro_Z |
5
|
-3.228
|
0.00443
|
-0.722
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.023 |
0.012 |
0.005 |
2.342 |
| HMC |
8 |
0.031 |
0.012 |
0.006 |
3.315 |
| HMC |
10 |
0.053 |
0.011 |
0.005 |
9.066 |
| HMC |
12 |
0.047 |
0.013 |
0.006 |
5.994 |
| HMC |
15 |
0.114 |
0.010 |
0.007 |
15.611 |
| HMC |
18 |
0.079 |
0.013 |
0.008 |
8.339 |
| SMC |
5 |
0.042 |
0.012 |
0.005 |
6.391 |
| SMC |
8 |
0.034 |
0.012 |
0.006 |
3.948 |
| SMC |
10 |
0.056 |
0.011 |
0.005 |
9.911 |
| SMC |
12 |
0.043 |
0.013 |
0.006 |
5.217 |
| SMC |
15 |
0.063 |
0.010 |
0.007 |
7.925 |
| SMC |
18 |
0.080 |
0.013 |
0.008 |
8.544 |
| Metro |
5 |
0.025 |
0.012 |
0.005 |
2.783 |
| Metro |
8 |
0.024 |
0.012 |
0.006 |
2.137 |
| Metro |
10 |
0.032 |
0.011 |
0.005 |
4.603 |
| Metro |
12 |
0.034 |
0.013 |
0.006 |
3.731 |
| Metro |
15 |
0.039 |
0.010 |
0.007 |
4.267 |
| Metro |
18 |
0.039 |
0.013 |
0.008 |
3.354 |
| DEMetro_Z |
5 |
0.037 |
0.012 |
0.005 |
5.217 |
| DEMetro_Z |
8 |
0.070 |
0.012 |
0.006 |
10.306 |
| DEMetro_Z |
10 |
0.054 |
0.011 |
0.005 |
9.391 |
| DEMetro_Z |
12 |
0.102 |
0.013 |
0.006 |
15.468 |
| DEMetro_Z |
15 |
0.148 |
0.010 |
0.007 |
20.757 |
| DEMetro_Z |
18 |
0.186 |
0.013 |
0.008 |
21.832 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.092 |
0.00452 |
1.585 |
| HMC |
8 |
4.470 |
0.000206 |
4.229 |
| HMC |
10 |
3.814 |
0.000704 |
1.942 |
| HMC |
12 |
4.460 |
0.000207 |
4.031 |
| HMC |
15 |
5.174 |
4.6e-05 |
7.193 |
| HMC |
18 |
4.742 |
0.00013 |
8.163 |
| SMC |
5 |
2.466 |
0.0188 |
0.947 |
| SMC |
8 |
4.868 |
8.27e-05 |
4.942 |
| SMC |
10 |
4.054 |
0.00057 |
4.033 |
| SMC |
12 |
3.199 |
0.0038 |
2.013 |
| SMC |
15 |
4.261 |
0.0004 |
8.090 |
| SMC |
18 |
4.200 |
0.000444 |
6.064 |
| Metro |
5 |
4.469 |
0.000116 |
2.195 |
| Metro |
8 |
4.678 |
7.9e-05 |
2.620 |
| Metro |
10 |
2.497 |
0.017 |
0.797 |
| Metro |
12 |
1.423 |
0.171 |
3.854 |
| Metro |
15 |
4.231 |
0.000384 |
4.575 |
| Metro |
18 |
4.352 |
0.000263 |
3.775 |
| DEMetro_Z |
5 |
3.702 |
0.00124 |
3.029 |
| DEMetro_Z |
8 |
4.424 |
0.000211 |
3.545 |
| DEMetro_Z |
10 |
4.512 |
0.000172 |
3.680 |
| DEMetro_Z |
12 |
4.874 |
9.34e-05 |
7.248 |
| DEMetro_Z |
15 |
4.433 |
0.000279 |
13.631 |
| DEMetro_Z |
18 |
6.099 |
6.46e-06 |
11.621 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.620
|
0.122
|
-0.362
|
| HMC_vs_DEMetro_Z |
1
|
0.533
|
0.6
|
0.119
|
| HMC_vs_DEMetro_Z |
2
|
-1.756
|
0.0951
|
-0.393
|
| HMC_vs_DEMetro_Z |
3
|
-1.945
|
0.0667
|
-0.435
|
| HMC_vs_DEMetro_Z |
4
|
-2.053
|
0.0541
|
-0.459
|
| HMC_vs_DEMetro_Z |
5
|
-1.264
|
0.222
|
-0.283
|
| Metro_vs_SMC |
0
|
2.476
|
0.0229
|
0.554
|
| Metro_vs_SMC |
1
|
-2.187
|
0.0414
|
-0.489
|
| Metro_vs_SMC |
2
|
-3.158
|
0.00518
|
-0.706
|
| Metro_vs_SMC |
3
|
0.669
|
0.512
|
0.149
|
| Metro_vs_SMC |
4
|
-1.561
|
0.135
|
-0.349
|
| Metro_vs_SMC |
5
|
-1.430
|
0.169
|
-0.320
|
| Metro_vs_DEMetro_Z |
0
|
-1.108
|
0.282
|
-0.248
|
| Metro_vs_DEMetro_Z |
1
|
-1.067
|
0.3
|
-0.238
|
| Metro_vs_DEMetro_Z |
2
|
-3.596
|
0.00193
|
-0.804
|
| Metro_vs_DEMetro_Z |
3
|
-0.996
|
0.332
|
-0.223
|
| Metro_vs_DEMetro_Z |
4
|
-2.823
|
0.0109
|
-0.631
|
| Metro_vs_DEMetro_Z |
5
|
-3.709
|
0.00149
|
-0.829
|
| HMC_vs_Metro |
0
|
-0.853
|
0.404
|
-0.191
|
| HMC_vs_Metro |
1
|
1.461
|
0.16
|
0.327
|
| HMC_vs_Metro |
2
|
2.492
|
0.0221
|
0.557
|
| HMC_vs_Metro |
3
|
0.058
|
0.954
|
0.013
|
| HMC_vs_Metro |
4
|
2.242
|
0.0371
|
0.501
|
| HMC_vs_Metro |
5
|
2.431
|
0.0251
|
0.544
|
| HMC_vs_SMC |
0
|
1.011
|
0.325
|
0.226
|
| HMC_vs_SMC |
1
|
-0.457
|
0.653
|
-0.102
|
| HMC_vs_SMC |
2
|
-2.024
|
0.0573
|
-0.453
|
| HMC_vs_SMC |
3
|
1.845
|
0.0806
|
0.413
|
| HMC_vs_SMC |
4
|
-0.374
|
0.713
|
-0.084
|
| HMC_vs_SMC |
5
|
0.916
|
0.371
|
0.205
|
| DEMetro_Z_vs_SMC |
0
|
2.481
|
0.0226
|
0.555
|
| DEMetro_Z_vs_SMC |
1
|
-1.061
|
0.302
|
-0.237
|
| DEMetro_Z_vs_SMC |
2
|
-0.286
|
0.778
|
-0.064
|
| DEMetro_Z_vs_SMC |
3
|
3.524
|
0.00227
|
0.788
|
| DEMetro_Z_vs_SMC |
4
|
1.380
|
0.184
|
0.309
|
| DEMetro_Z_vs_SMC |
5
|
2.356
|
0.0294
|
0.527
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.111 |
0.053 |
0.036 |
1.585 |
| HMC |
8 |
0.242 |
0.058 |
0.044 |
4.229 |
| HMC |
10 |
0.313 |
0.096 |
0.112 |
1.942 |
| HMC |
12 |
0.366 |
0.108 |
0.064 |
4.031 |
| HMC |
15 |
0.646 |
0.113 |
0.074 |
7.193 |
| HMC |
18 |
1.034 |
0.135 |
0.110 |
8.163 |
| SMC |
5 |
0.088 |
0.053 |
0.036 |
0.947 |
| SMC |
8 |
0.273 |
0.058 |
0.044 |
4.942 |
| SMC |
10 |
0.547 |
0.096 |
0.112 |
4.033 |
| SMC |
12 |
0.236 |
0.108 |
0.064 |
2.013 |
| SMC |
15 |
0.713 |
0.113 |
0.074 |
8.090 |
| SMC |
18 |
0.803 |
0.135 |
0.110 |
6.064 |
| Metro |
5 |
0.133 |
0.053 |
0.036 |
2.195 |
| Metro |
8 |
0.172 |
0.058 |
0.044 |
2.620 |
| Metro |
10 |
0.185 |
0.096 |
0.112 |
0.797 |
| Metro |
12 |
0.354 |
0.108 |
0.064 |
3.854 |
| Metro |
15 |
0.452 |
0.113 |
0.074 |
4.575 |
| Metro |
18 |
0.551 |
0.135 |
0.110 |
3.775 |
| DEMetro_Z |
5 |
0.163 |
0.053 |
0.036 |
3.029 |
| DEMetro_Z |
8 |
0.213 |
0.058 |
0.044 |
3.545 |
| DEMetro_Z |
10 |
0.507 |
0.096 |
0.112 |
3.680 |
| DEMetro_Z |
12 |
0.571 |
0.108 |
0.064 |
7.248 |
| DEMetro_Z |
15 |
1.124 |
0.113 |
0.074 |
13.631 |
| DEMetro_Z |
18 |
1.415 |
0.135 |
0.110 |
11.621 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
-1.420 |
0.171 |
-0.320 |
| HMC |
8 |
1.283 |
0.21 |
0.664 |
| HMC |
10 |
-0.800 |
0.433 |
-0.182 |
| HMC |
12 |
-1.313 |
0.204 |
-0.296 |
| HMC |
15 |
-0.899 |
0.378 |
-0.211 |
| HMC |
18 |
0.674 |
0.505 |
0.206 |
| SMC |
5 |
-1.610 |
0.124 |
-0.360 |
| SMC |
8 |
0.647 |
0.522 |
0.290 |
| SMC |
10 |
-0.785 |
0.442 |
-0.179 |
| SMC |
12 |
-1.477 |
0.156 |
-0.333 |
| SMC |
15 |
-0.735 |
0.47 |
-0.169 |
| SMC |
18 |
-0.120 |
0.905 |
-0.031 |
| Metro |
5 |
-1.534 |
0.141 |
-0.344 |
| Metro |
8 |
2.460 |
0.0208 |
1.349 |
| Metro |
10 |
-0.792 |
0.437 |
-0.181 |
| Metro |
12 |
0.160 |
0.874 |
0.071 |
| Metro |
15 |
0.174 |
0.863 |
0.069 |
| Metro |
18 |
-0.192 |
0.849 |
-0.052 |
| DEMetro_Z |
5 |
-1.437 |
0.167 |
-0.323 |
| DEMetro_Z |
8 |
1.794 |
0.0844 |
1.002 |
| DEMetro_Z |
10 |
-0.690 |
0.498 |
-0.158 |
| DEMetro_Z |
12 |
-1.377 |
0.184 |
-0.310 |
| DEMetro_Z |
15 |
0.027 |
0.978 |
0.007 |
| DEMetro_Z |
18 |
1.494 |
0.143 |
0.480 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.331
|
0.199
|
0.298
|
| HMC_vs_SMC |
1
|
1.986
|
0.0617
|
0.444
|
| HMC_vs_SMC |
2
|
-2.306
|
0.0325
|
-0.516
|
| HMC_vs_SMC |
3
|
1.808
|
0.0865
|
0.404
|
| HMC_vs_SMC |
4
|
-0.588
|
0.563
|
-0.132
|
| HMC_vs_SMC |
5
|
0.940
|
0.359
|
0.210
|
| Metro_vs_DEMetro_Z |
0
|
-1.862
|
0.0781
|
-0.416
|
| Metro_vs_DEMetro_Z |
1
|
1.173
|
0.255
|
0.262
|
| Metro_vs_DEMetro_Z |
2
|
-1.093
|
0.288
|
-0.244
|
| Metro_vs_DEMetro_Z |
3
|
1.016
|
0.322
|
0.227
|
| Metro_vs_DEMetro_Z |
4
|
0.174
|
0.864
|
0.039
|
| Metro_vs_DEMetro_Z |
5
|
-2.118
|
0.0476
|
-0.474
|
| HMC_vs_Metro |
0
|
0.801
|
0.433
|
0.179
|
| HMC_vs_Metro |
1
|
-2.373
|
0.0283
|
-0.531
|
| HMC_vs_Metro |
2
|
-1.423
|
0.171
|
-0.318
|
| HMC_vs_Metro |
3
|
-0.979
|
0.34
|
-0.219
|
| HMC_vs_Metro |
4
|
-0.864
|
0.398
|
-0.193
|
| HMC_vs_Metro |
5
|
0.938
|
0.36
|
0.210
|
| HMC_vs_DEMetro_Z |
0
|
0.079
|
0.938
|
0.018
|
| HMC_vs_DEMetro_Z |
1
|
-2.074
|
0.0519
|
-0.464
|
| HMC_vs_DEMetro_Z |
2
|
-1.182
|
0.252
|
-0.264
|
| HMC_vs_DEMetro_Z |
3
|
0.827
|
0.418
|
0.185
|
| HMC_vs_DEMetro_Z |
4
|
-1.849
|
0.0801
|
-0.413
|
| HMC_vs_DEMetro_Z |
5
|
-0.856
|
0.403
|
-0.191
|
| Metro_vs_SMC |
0
|
0.993
|
0.333
|
0.222
|
| Metro_vs_SMC |
1
|
3.992
|
0.000781
|
0.893
|
| Metro_vs_SMC |
2
|
-1.259
|
0.223
|
-0.281
|
| Metro_vs_SMC |
3
|
1.077
|
0.295
|
0.241
|
| Metro_vs_SMC |
4
|
0.707
|
0.488
|
0.158
|
| Metro_vs_SMC |
5
|
-0.106
|
0.917
|
-0.024
|
| DEMetro_Z_vs_SMC |
0
|
2.212
|
0.0394
|
0.495
|
| DEMetro_Z_vs_SMC |
1
|
3.983
|
0.000797
|
0.891
|
| DEMetro_Z_vs_SMC |
2
|
0.995
|
0.332
|
0.222
|
| DEMetro_Z_vs_SMC |
3
|
1.607
|
0.124
|
0.359
|
| DEMetro_Z_vs_SMC |
4
|
1.429
|
0.169
|
0.320
|
| DEMetro_Z_vs_SMC |
5
|
2.039
|
0.0556
|
0.456
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
4.368 |
17.284 |
40.350 |
-0.320 |
| HMC |
8 |
4.999 |
3.215 |
2.688 |
0.664 |
| HMC |
10 |
19.988 |
87.229 |
368.626 |
-0.182 |
| HMC |
12 |
6.044 |
19.100 |
44.067 |
-0.296 |
| HMC |
15 |
5.639 |
8.635 |
14.171 |
-0.211 |
| HMC |
18 |
6.807 |
5.445 |
6.620 |
0.206 |
| SMC |
5 |
2.746 |
17.284 |
40.350 |
-0.360 |
| SMC |
8 |
3.994 |
3.215 |
2.688 |
0.290 |
| SMC |
10 |
21.277 |
87.229 |
368.626 |
-0.179 |
| SMC |
12 |
4.438 |
19.100 |
44.067 |
-0.333 |
| SMC |
15 |
6.237 |
8.635 |
14.171 |
-0.169 |
| SMC |
18 |
5.240 |
5.445 |
6.620 |
-0.031 |
| Metro |
5 |
3.403 |
17.284 |
40.350 |
-0.344 |
| Metro |
8 |
6.842 |
3.215 |
2.688 |
1.349 |
| Metro |
10 |
20.615 |
87.229 |
368.626 |
-0.181 |
| Metro |
12 |
22.222 |
19.100 |
44.067 |
0.071 |
| Metro |
15 |
9.609 |
8.635 |
14.171 |
0.069 |
| Metro |
18 |
5.104 |
5.445 |
6.620 |
-0.052 |
| DEMetro_Z |
5 |
4.271 |
17.284 |
40.350 |
-0.323 |
| DEMetro_Z |
8 |
5.907 |
3.215 |
2.688 |
1.002 |
| DEMetro_Z |
10 |
28.997 |
87.229 |
368.626 |
-0.158 |
| DEMetro_Z |
12 |
5.432 |
19.100 |
44.067 |
-0.310 |
| DEMetro_Z |
15 |
8.735 |
8.635 |
14.171 |
0.007 |
| DEMetro_Z |
18 |
8.625 |
5.445 |
6.620 |
0.480 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
2.357 |
0.0239 |
0.846 |
| HMC |
8 |
5.578 |
1.58e-05 |
5.699 |
| HMC |
10 |
3.912 |
0.000483 |
1.767 |
| HMC |
12 |
4.636 |
0.000129 |
3.904 |
| HMC |
15 |
5.263 |
3.86e-05 |
7.941 |
| HMC |
18 |
4.881 |
9.79e-05 |
10.499 |
| SMC |
5 |
2.862 |
0.00689 |
0.987 |
| SMC |
8 |
7.341 |
3.24e-07 |
7.457 |
| SMC |
10 |
5.284 |
2.83e-05 |
4.700 |
| SMC |
12 |
5.994 |
2.44e-06 |
3.312 |
| SMC |
15 |
5.445 |
2.7e-05 |
10.352 |
| SMC |
18 |
5.724 |
1.38e-05 |
8.855 |
| Metro |
5 |
4.700 |
3.65e-05 |
1.669 |
| Metro |
8 |
8.181 |
9.65e-09 |
4.392 |
| Metro |
10 |
3.395 |
0.00176 |
0.927 |
| Metro |
12 |
1.631 |
0.119 |
4.778 |
| Metro |
15 |
4.879 |
8.24e-05 |
5.196 |
| Metro |
18 |
4.984 |
6.04e-05 |
4.720 |
| DEMetro_Z |
5 |
4.927 |
3.22e-05 |
2.388 |
| DEMetro_Z |
8 |
5.619 |
1.5e-05 |
6.139 |
| DEMetro_Z |
10 |
4.692 |
0.000111 |
3.856 |
| DEMetro_Z |
12 |
5.269 |
3.69e-05 |
7.191 |
| DEMetro_Z |
15 |
4.874 |
0.000102 |
15.114 |
| DEMetro_Z |
18 |
6.422 |
3.39e-06 |
14.919 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-1.438
|
0.167
|
-0.321
|
| Metro_vs_DEMetro_Z |
1
|
-1.411
|
0.174
|
-0.315
|
| Metro_vs_DEMetro_Z |
2
|
-3.605
|
0.00189
|
-0.806
|
| Metro_vs_DEMetro_Z |
3
|
-0.692
|
0.497
|
-0.155
|
| Metro_vs_DEMetro_Z |
4
|
-3.079
|
0.00618
|
-0.689
|
| Metro_vs_DEMetro_Z |
5
|
-4.296
|
0.00039
|
-0.961
|
| DEMetro_Z_vs_SMC |
0
|
3.655
|
0.00168
|
0.817
|
| DEMetro_Z_vs_SMC |
1
|
-0.995
|
0.332
|
-0.223
|
| DEMetro_Z_vs_SMC |
2
|
-0.707
|
0.488
|
-0.158
|
| DEMetro_Z_vs_SMC |
3
|
2.710
|
0.0139
|
0.606
|
| DEMetro_Z_vs_SMC |
4
|
1.173
|
0.255
|
0.262
|
| DEMetro_Z_vs_SMC |
5
|
2.211
|
0.0395
|
0.494
|
| HMC_vs_DEMetro_Z |
0
|
-2.772
|
0.0121
|
-0.620
|
| HMC_vs_DEMetro_Z |
1
|
-0.277
|
0.784
|
-0.062
|
| HMC_vs_DEMetro_Z |
2
|
-2.249
|
0.0366
|
-0.503
|
| HMC_vs_DEMetro_Z |
3
|
-2.083
|
0.051
|
-0.466
|
| HMC_vs_DEMetro_Z |
4
|
-2.276
|
0.0346
|
-0.509
|
| HMC_vs_DEMetro_Z |
5
|
-1.278
|
0.217
|
-0.286
|
| HMC_vs_Metro |
0
|
-1.915
|
0.0706
|
-0.428
|
| HMC_vs_Metro |
1
|
1.178
|
0.253
|
0.263
|
| HMC_vs_Metro |
2
|
2.086
|
0.0507
|
0.466
|
| HMC_vs_Metro |
3
|
-0.281
|
0.782
|
-0.063
|
| HMC_vs_Metro |
4
|
2.200
|
0.0404
|
0.492
|
| HMC_vs_Metro |
5
|
2.497
|
0.0219
|
0.558
|
| HMC_vs_SMC |
0
|
-0.347
|
0.733
|
-0.078
|
| HMC_vs_SMC |
1
|
-1.059
|
0.303
|
-0.237
|
| HMC_vs_SMC |
2
|
-3.121
|
0.00562
|
-0.698
|
| HMC_vs_SMC |
3
|
0.591
|
0.561
|
0.132
|
| HMC_vs_SMC |
4
|
-0.940
|
0.359
|
-0.210
|
| HMC_vs_SMC |
5
|
0.634
|
0.534
|
0.142
|
| Metro_vs_SMC |
0
|
2.191
|
0.0411
|
0.490
|
| Metro_vs_SMC |
1
|
-2.736
|
0.0131
|
-0.612
|
| Metro_vs_SMC |
2
|
-4.177
|
0.000511
|
-0.934
|
| Metro_vs_SMC |
3
|
0.494
|
0.627
|
0.110
|
| Metro_vs_SMC |
4
|
-2.230
|
0.038
|
-0.499
|
| Metro_vs_SMC |
5
|
-2.393
|
0.0272
|
-0.535
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.183 |
0.135 |
0.057 |
0.846 |
| HMC |
8 |
0.325 |
0.133 |
0.034 |
5.699 |
| HMC |
10 |
0.369 |
0.171 |
0.112 |
1.767 |
| HMC |
12 |
0.427 |
0.191 |
0.060 |
3.904 |
| HMC |
15 |
0.694 |
0.176 |
0.065 |
7.941 |
| HMC |
18 |
1.036 |
0.213 |
0.078 |
10.499 |
| SMC |
5 |
0.191 |
0.135 |
0.057 |
0.987 |
| SMC |
8 |
0.384 |
0.133 |
0.034 |
7.457 |
| SMC |
10 |
0.698 |
0.171 |
0.112 |
4.700 |
| SMC |
12 |
0.391 |
0.191 |
0.060 |
3.312 |
| SMC |
15 |
0.851 |
0.176 |
0.065 |
10.352 |
| SMC |
18 |
0.907 |
0.213 |
0.078 |
8.855 |
| Metro |
5 |
0.230 |
0.135 |
0.057 |
1.669 |
| Metro |
8 |
0.281 |
0.133 |
0.034 |
4.392 |
| Metro |
10 |
0.275 |
0.171 |
0.112 |
0.927 |
| Metro |
12 |
0.480 |
0.191 |
0.060 |
4.778 |
| Metro |
15 |
0.515 |
0.176 |
0.065 |
5.196 |
| Metro |
18 |
0.583 |
0.213 |
0.078 |
4.720 |
| DEMetro_Z |
5 |
0.271 |
0.135 |
0.057 |
2.388 |
| DEMetro_Z |
8 |
0.340 |
0.133 |
0.034 |
6.139 |
| DEMetro_Z |
10 |
0.603 |
0.171 |
0.112 |
3.856 |
| DEMetro_Z |
12 |
0.626 |
0.191 |
0.060 |
7.191 |
| DEMetro_Z |
15 |
1.162 |
0.176 |
0.065 |
15.114 |
| DEMetro_Z |
18 |
1.382 |
0.213 |
0.078 |
14.919 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.091 |
0.000447 |
2.937 |
| HMC |
8 |
4.443 |
0.000251 |
6.284 |
| HMC |
10 |
4.734 |
0.000132 |
7.895 |
| HMC |
12 |
4.979 |
6.81e-05 |
5.877 |
| HMC |
15 |
5.151 |
5.1e-05 |
8.626 |
| HMC |
18 |
4.686 |
0.000153 |
10.539 |
| SMC |
5 |
4.028 |
0.000513 |
2.793 |
| SMC |
8 |
5.435 |
2.53e-05 |
7.426 |
| SMC |
10 |
4.664 |
0.000166 |
17.094 |
| SMC |
12 |
4.749 |
9.82e-05 |
3.993 |
| SMC |
15 |
4.235 |
0.000435 |
10.728 |
| SMC |
18 |
4.208 |
0.000453 |
8.150 |
| Metro |
5 |
5.770 |
6.01e-06 |
3.753 |
| Metro |
8 |
4.589 |
0.0001 |
2.581 |
| Metro |
10 |
4.842 |
5.32e-05 |
2.785 |
| Metro |
12 |
4.248 |
0.000249 |
2.421 |
| Metro |
15 |
4.611 |
0.000143 |
4.155 |
| Metro |
18 |
4.408 |
0.000241 |
4.261 |
| DEMetro_Z |
5 |
5.098 |
3.33e-05 |
3.389 |
| DEMetro_Z |
8 |
4.375 |
0.000274 |
4.762 |
| DEMetro_Z |
10 |
5.480 |
2.5e-05 |
10.399 |
| DEMetro_Z |
12 |
4.511 |
0.000229 |
10.400 |
| DEMetro_Z |
15 |
4.238 |
0.00044 |
17.736 |
| DEMetro_Z |
18 |
5.481 |
2.63e-05 |
15.224 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
0.817
|
0.424
|
0.183
|
| DEMetro_Z_vs_SMC |
1
|
-1.578
|
0.131
|
-0.353
|
| DEMetro_Z_vs_SMC |
2
|
-1.861
|
0.0783
|
-0.416
|
| DEMetro_Z_vs_SMC |
3
|
2.753
|
0.0126
|
0.616
|
| DEMetro_Z_vs_SMC |
4
|
1.284
|
0.215
|
0.287
|
| DEMetro_Z_vs_SMC |
5
|
2.088
|
0.0505
|
0.467
|
| HMC_vs_Metro |
0
|
-0.808
|
0.429
|
-0.181
|
| HMC_vs_Metro |
1
|
2.631
|
0.0165
|
0.588
|
| HMC_vs_Metro |
2
|
3.212
|
0.00458
|
0.718
|
| HMC_vs_Metro |
3
|
2.763
|
0.0124
|
0.618
|
| HMC_vs_Metro |
4
|
2.912
|
0.00894
|
0.651
|
| HMC_vs_Metro |
5
|
2.674
|
0.015
|
0.598
|
| Metro_vs_DEMetro_Z |
0
|
0.450
|
0.657
|
0.101
|
| Metro_vs_DEMetro_Z |
1
|
-1.843
|
0.081
|
-0.412
|
| Metro_vs_DEMetro_Z |
2
|
-4.296
|
0.00039
|
-0.961
|
| Metro_vs_DEMetro_Z |
3
|
-3.282
|
0.00392
|
-0.734
|
| Metro_vs_DEMetro_Z |
4
|
-3.292
|
0.00383
|
-0.736
|
| Metro_vs_DEMetro_Z |
5
|
-3.925
|
0.00091
|
-0.878
|
| HMC_vs_SMC |
0
|
0.142
|
0.889
|
0.032
|
| HMC_vs_SMC |
1
|
-0.507
|
0.618
|
-0.113
|
| HMC_vs_SMC |
2
|
-2.297
|
0.0331
|
-0.514
|
| HMC_vs_SMC |
3
|
1.280
|
0.216
|
0.286
|
| HMC_vs_SMC |
4
|
-0.663
|
0.515
|
-0.148
|
| HMC_vs_SMC |
5
|
0.788
|
0.44
|
0.176
|
| Metro_vs_SMC |
0
|
1.140
|
0.268
|
0.255
|
| Metro_vs_SMC |
1
|
-3.724
|
0.00144
|
-0.833
|
| Metro_vs_SMC |
2
|
-3.691
|
0.00155
|
-0.825
|
| Metro_vs_SMC |
3
|
-1.415
|
0.173
|
-0.317
|
| Metro_vs_SMC |
4
|
-2.253
|
0.0363
|
-0.504
|
| Metro_vs_SMC |
5
|
-1.877
|
0.0759
|
-0.420
|
| HMC_vs_DEMetro_Z |
0
|
-0.418
|
0.681
|
-0.093
|
| HMC_vs_DEMetro_Z |
1
|
0.782
|
0.444
|
0.175
|
| HMC_vs_DEMetro_Z |
2
|
-0.998
|
0.331
|
-0.223
|
| HMC_vs_DEMetro_Z |
3
|
-1.771
|
0.0927
|
-0.396
|
| HMC_vs_DEMetro_Z |
4
|
-2.206
|
0.0399
|
-0.493
|
| HMC_vs_DEMetro_Z |
5
|
-1.209
|
0.241
|
-0.270
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.026 |
0.012 |
0.005 |
2.937 |
| HMC |
8 |
0.047 |
0.012 |
0.006 |
6.284 |
| HMC |
10 |
0.047 |
0.011 |
0.005 |
7.895 |
| HMC |
12 |
0.047 |
0.013 |
0.006 |
5.877 |
| HMC |
15 |
0.067 |
0.010 |
0.007 |
8.626 |
| HMC |
18 |
0.096 |
0.013 |
0.008 |
10.539 |
| SMC |
5 |
0.025 |
0.012 |
0.005 |
2.793 |
| SMC |
8 |
0.054 |
0.012 |
0.006 |
7.426 |
| SMC |
10 |
0.090 |
0.011 |
0.005 |
17.094 |
| SMC |
12 |
0.036 |
0.013 |
0.006 |
3.993 |
| SMC |
15 |
0.081 |
0.010 |
0.007 |
10.728 |
| SMC |
18 |
0.077 |
0.013 |
0.008 |
8.150 |
| Metro |
5 |
0.030 |
0.012 |
0.005 |
3.753 |
| Metro |
8 |
0.027 |
0.012 |
0.006 |
2.581 |
| Metro |
10 |
0.024 |
0.011 |
0.005 |
2.785 |
| Metro |
12 |
0.027 |
0.013 |
0.006 |
2.421 |
| Metro |
15 |
0.038 |
0.010 |
0.007 |
4.155 |
| Metro |
18 |
0.047 |
0.013 |
0.008 |
4.261 |
| DEMetro_Z |
5 |
0.028 |
0.012 |
0.005 |
3.389 |
| DEMetro_Z |
8 |
0.039 |
0.012 |
0.006 |
4.762 |
| DEMetro_Z |
10 |
0.059 |
0.011 |
0.005 |
10.399 |
| DEMetro_Z |
12 |
0.073 |
0.013 |
0.006 |
10.400 |
| DEMetro_Z |
15 |
0.128 |
0.010 |
0.007 |
17.736 |
| DEMetro_Z |
18 |
0.133 |
0.013 |
0.008 |
15.224 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_only_Tails
(MvStudentT,
nu,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.051 |
0.96 |
-0.016 |
| HMC |
3.0 |
1.689 |
0.0996 |
0.574 |
| HMC |
4.0 |
-0.465 |
0.645 |
-0.152 |
| HMC |
10.0 |
-0.383 |
0.704 |
-0.110 |
| HMC |
50.0 |
-1.990 |
0.0545 |
-0.549 |
| SMC |
2.1 |
2.419 |
0.0219 |
1.109 |
| SMC |
3.0 |
-0.368 |
0.715 |
-0.119 |
| SMC |
4.0 |
1.279 |
0.209 |
0.416 |
| SMC |
10.0 |
-1.027 |
0.311 |
-0.298 |
| SMC |
50.0 |
-1.388 |
0.174 |
-0.386 |
| Metro |
2.1 |
1.569 |
0.125 |
0.538 |
| Metro |
3.0 |
2.606 |
0.0139 |
1.114 |
| Metro |
4.0 |
3.390 |
0.00241 |
2.192 |
| Metro |
10.0 |
2.411 |
0.0209 |
0.741 |
| Metro |
50.0 |
1.668 |
0.105 |
0.662 |
| DEMetro_Z |
2.1 |
4.029 |
0.000387 |
1.999 |
| DEMetro_Z |
3.0 |
3.095 |
0.00472 |
1.780 |
| DEMetro_Z |
4.0 |
4.502 |
0.000118 |
2.400 |
| DEMetro_Z |
10.0 |
2.991 |
0.00591 |
1.595 |
| DEMetro_Z |
50.0 |
3.205 |
0.00311 |
1.392 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-5.007
|
7.83e-05
|
-1.120
|
| HMC_vs_DEMetro_Z |
1
|
-1.916
|
0.0705
|
-0.428
|
| HMC_vs_DEMetro_Z |
2
|
-4.854
|
0.00011
|
-1.085
|
| HMC_vs_DEMetro_Z |
3
|
-3.145
|
0.00533
|
-0.703
|
| HMC_vs_DEMetro_Z |
4
|
-4.781
|
0.00013
|
-1.069
|
| Metro_vs_SMC |
0
|
-1.329
|
0.2
|
-0.297
|
| Metro_vs_SMC |
1
|
3.063
|
0.0064
|
0.685
|
| Metro_vs_SMC |
2
|
2.531
|
0.0203
|
0.566
|
| Metro_vs_SMC |
3
|
4.466
|
0.000265
|
0.999
|
| Metro_vs_SMC |
4
|
3.438
|
0.00275
|
0.769
|
| Metro_vs_DEMetro_Z |
0
|
-2.945
|
0.00831
|
-0.659
|
| Metro_vs_DEMetro_Z |
1
|
-0.933
|
0.363
|
-0.209
|
| Metro_vs_DEMetro_Z |
2
|
-0.256
|
0.801
|
-0.057
|
| Metro_vs_DEMetro_Z |
3
|
-1.778
|
0.0914
|
-0.398
|
| Metro_vs_DEMetro_Z |
4
|
-1.555
|
0.137
|
-0.348
|
| HMC_vs_Metro |
0
|
-1.601
|
0.126
|
-0.358
|
| HMC_vs_Metro |
1
|
-1.140
|
0.268
|
-0.255
|
| HMC_vs_Metro |
2
|
-3.505
|
0.00237
|
-0.784
|
| HMC_vs_Metro |
3
|
-3.623
|
0.00181
|
-0.810
|
| HMC_vs_Metro |
4
|
-3.557
|
0.00211
|
-0.795
|
| HMC_vs_SMC |
0
|
-3.306
|
0.00371
|
-0.739
|
| HMC_vs_SMC |
1
|
2.370
|
0.0285
|
0.530
|
| HMC_vs_SMC |
2
|
-2.594
|
0.0178
|
-0.580
|
| HMC_vs_SMC |
3
|
0.674
|
0.508
|
0.151
|
| HMC_vs_SMC |
4
|
-0.932
|
0.363
|
-0.208
|
| DEMetro_Z_vs_SMC |
0
|
1.522
|
0.145
|
0.340
|
| DEMetro_Z_vs_SMC |
1
|
3.365
|
0.00325
|
0.752
|
| DEMetro_Z_vs_SMC |
2
|
3.577
|
0.00201
|
0.800
|
| DEMetro_Z_vs_SMC |
3
|
3.756
|
0.00134
|
0.840
|
| DEMetro_Z_vs_SMC |
4
|
4.436
|
0.000284
|
0.992
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.066 |
0.066 |
0.039 |
-0.016 |
| HMC |
3.0 |
0.053 |
0.039 |
0.023 |
0.574 |
| HMC |
4.0 |
0.026 |
0.028 |
0.014 |
-0.152 |
| HMC |
10.0 |
0.025 |
0.026 |
0.015 |
-0.110 |
| HMC |
50.0 |
0.017 |
0.024 |
0.013 |
-0.549 |
| SMC |
2.1 |
0.110 |
0.066 |
0.039 |
1.109 |
| SMC |
3.0 |
0.037 |
0.039 |
0.023 |
-0.119 |
| SMC |
4.0 |
0.034 |
0.028 |
0.014 |
0.416 |
| SMC |
10.0 |
0.022 |
0.026 |
0.015 |
-0.298 |
| SMC |
50.0 |
0.019 |
0.024 |
0.013 |
-0.386 |
| Metro |
2.1 |
0.087 |
0.066 |
0.039 |
0.538 |
| Metro |
3.0 |
0.065 |
0.039 |
0.023 |
1.114 |
| Metro |
4.0 |
0.058 |
0.028 |
0.014 |
2.192 |
| Metro |
10.0 |
0.037 |
0.026 |
0.015 |
0.741 |
| Metro |
50.0 |
0.032 |
0.024 |
0.013 |
0.662 |
| DEMetro_Z |
2.1 |
0.145 |
0.066 |
0.039 |
1.999 |
| DEMetro_Z |
3.0 |
0.081 |
0.039 |
0.023 |
1.780 |
| DEMetro_Z |
4.0 |
0.061 |
0.028 |
0.014 |
2.400 |
| DEMetro_Z |
10.0 |
0.050 |
0.026 |
0.015 |
1.595 |
| DEMetro_Z |
50.0 |
0.041 |
0.024 |
0.013 |
1.392 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.219 |
0.828 |
-0.061 |
| HMC |
3.0 |
0.599 |
0.553 |
0.227 |
| HMC |
4.0 |
-0.847 |
0.403 |
-0.227 |
| HMC |
10.0 |
2.358 |
0.0239 |
0.839 |
| HMC |
50.0 |
0.819 |
0.418 |
0.263 |
| SMC |
2.1 |
1.601 |
0.119 |
0.422 |
| SMC |
3.0 |
-0.680 |
0.501 |
-0.200 |
| SMC |
4.0 |
-1.337 |
0.192 |
-0.335 |
| SMC |
10.0 |
-0.400 |
0.691 |
-0.134 |
| SMC |
50.0 |
-1.777 |
0.0848 |
-0.477 |
| Metro |
2.1 |
-0.735 |
0.468 |
-0.196 |
| Metro |
3.0 |
1.233 |
0.226 |
0.521 |
| Metro |
4.0 |
1.576 |
0.125 |
0.692 |
| Metro |
10.0 |
4.584 |
6.08e-05 |
1.823 |
| Metro |
50.0 |
2.139 |
0.04 |
0.877 |
| DEMetro_Z |
2.1 |
-0.475 |
0.638 |
-0.127 |
| DEMetro_Z |
3.0 |
3.309 |
0.00216 |
1.228 |
| DEMetro_Z |
4.0 |
2.627 |
0.0124 |
0.793 |
| DEMetro_Z |
10.0 |
5.582 |
8.33e-06 |
3.342 |
| DEMetro_Z |
50.0 |
3.102 |
0.00368 |
1.086 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-2.563
|
0.019
|
-0.573
|
| HMC_vs_SMC |
1
|
1.508
|
0.148
|
0.337
|
| HMC_vs_SMC |
2
|
0.576
|
0.571
|
0.129
|
| HMC_vs_SMC |
3
|
3.169
|
0.00506
|
0.709
|
| HMC_vs_SMC |
4
|
2.850
|
0.0102
|
0.637
|
| Metro_vs_DEMetro_Z |
0
|
-1.364
|
0.189
|
-0.305
|
| Metro_vs_DEMetro_Z |
1
|
-1.898
|
0.073
|
-0.424
|
| Metro_vs_DEMetro_Z |
2
|
-0.253
|
0.803
|
-0.056
|
| Metro_vs_DEMetro_Z |
3
|
-2.292
|
0.0335
|
-0.512
|
| Metro_vs_DEMetro_Z |
4
|
-0.484
|
0.634
|
-0.108
|
| HMC_vs_Metro |
0
|
1.358
|
0.19
|
0.304
|
| HMC_vs_Metro |
1
|
-0.621
|
0.542
|
-0.139
|
| HMC_vs_Metro |
2
|
-3.045
|
0.00666
|
-0.681
|
| HMC_vs_Metro |
3
|
-2.027
|
0.0569
|
-0.453
|
| HMC_vs_Metro |
4
|
-1.339
|
0.196
|
-0.299
|
| HMC_vs_DEMetro_Z |
0
|
0.597
|
0.558
|
0.133
|
| HMC_vs_DEMetro_Z |
1
|
-2.487
|
0.0224
|
-0.556
|
| HMC_vs_DEMetro_Z |
2
|
-3.639
|
0.00175
|
-0.814
|
| HMC_vs_DEMetro_Z |
3
|
-4.698
|
0.000157
|
-1.051
|
| HMC_vs_DEMetro_Z |
4
|
-1.977
|
0.0627
|
-0.442
|
| Metro_vs_SMC |
0
|
-3.309
|
0.00369
|
-0.740
|
| Metro_vs_SMC |
1
|
2.152
|
0.0445
|
0.481
|
| Metro_vs_SMC |
2
|
2.748
|
0.0128
|
0.615
|
| Metro_vs_SMC |
3
|
5.474
|
2.79e-05
|
1.224
|
| Metro_vs_SMC |
4
|
3.781
|
0.00126
|
0.845
|
| DEMetro_Z_vs_SMC |
0
|
-2.785
|
0.0118
|
-0.623
|
| DEMetro_Z_vs_SMC |
1
|
5.466
|
2.84e-05
|
1.222
|
| DEMetro_Z_vs_SMC |
2
|
5.405
|
3.24e-05
|
1.209
|
| DEMetro_Z_vs_SMC |
3
|
5.961
|
9.76e-06
|
1.333
|
| DEMetro_Z_vs_SMC |
4
|
4.717
|
0.00015
|
1.055
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
8.387 |
9.309 |
15.244 |
-0.061 |
| HMC |
3.0 |
0.650 |
0.552 |
0.433 |
0.227 |
| HMC |
4.0 |
0.142 |
0.173 |
0.139 |
-0.227 |
| HMC |
10.0 |
0.057 |
0.040 |
0.020 |
0.839 |
| HMC |
50.0 |
0.036 |
0.031 |
0.019 |
0.263 |
| SMC |
2.1 |
15.738 |
9.309 |
15.244 |
0.422 |
| SMC |
3.0 |
0.466 |
0.552 |
0.433 |
-0.200 |
| SMC |
4.0 |
0.127 |
0.173 |
0.139 |
-0.335 |
| SMC |
10.0 |
0.037 |
0.040 |
0.020 |
-0.134 |
| SMC |
50.0 |
0.022 |
0.031 |
0.019 |
-0.477 |
| Metro |
2.1 |
6.327 |
9.309 |
15.244 |
-0.196 |
| Metro |
3.0 |
0.778 |
0.552 |
0.433 |
0.521 |
| Metro |
4.0 |
0.269 |
0.173 |
0.139 |
0.692 |
| Metro |
10.0 |
0.077 |
0.040 |
0.020 |
1.823 |
| Metro |
50.0 |
0.047 |
0.031 |
0.019 |
0.877 |
| DEMetro_Z |
2.1 |
7.372 |
9.309 |
15.244 |
-0.127 |
| DEMetro_Z |
3.0 |
1.084 |
0.552 |
0.433 |
1.228 |
| DEMetro_Z |
4.0 |
0.283 |
0.173 |
0.139 |
0.793 |
| DEMetro_Z |
10.0 |
0.107 |
0.040 |
0.020 |
3.342 |
| DEMetro_Z |
50.0 |
0.051 |
0.031 |
0.019 |
1.086 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.228 |
0.0346 |
1.224 |
| HMC |
3.0 |
1.828 |
0.0794 |
1.075 |
| HMC |
4.0 |
1.797 |
0.0821 |
0.791 |
| HMC |
10.0 |
0.051 |
0.96 |
0.015 |
| HMC |
50.0 |
-0.802 |
0.428 |
-0.220 |
| SMC |
2.1 |
8.900 |
2.84e-08 |
20.527 |
| SMC |
3.0 |
1.513 |
0.141 |
0.680 |
| SMC |
4.0 |
0.230 |
0.82 |
0.094 |
| SMC |
10.0 |
-1.521 |
0.138 |
-0.411 |
| SMC |
50.0 |
-1.491 |
0.145 |
-0.402 |
| Metro |
2.1 |
4.573 |
5.32e-05 |
1.610 |
| Metro |
3.0 |
5.885 |
4.9e-06 |
4.007 |
| Metro |
4.0 |
5.749 |
9.22e-06 |
4.966 |
| Metro |
10.0 |
5.678 |
1.58e-06 |
1.833 |
| Metro |
50.0 |
3.747 |
0.000615 |
1.318 |
| DEMetro_Z |
2.1 |
6.933 |
2.84e-07 |
4.132 |
| DEMetro_Z |
3.0 |
7.913 |
5.97e-08 |
6.043 |
| DEMetro_Z |
4.0 |
9.405 |
2.41e-09 |
6.787 |
| DEMetro_Z |
10.0 |
6.227 |
1.38e-06 |
3.477 |
| DEMetro_Z |
50.0 |
5.980 |
1.12e-06 |
2.493 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-4.905
|
9.83e-05
|
-1.097
|
| Metro_vs_DEMetro_Z |
1
|
-2.044
|
0.055
|
-0.457
|
| Metro_vs_DEMetro_Z |
2
|
-1.722
|
0.101
|
-0.385
|
| Metro_vs_DEMetro_Z |
3
|
-3.123
|
0.0056
|
-0.698
|
| Metro_vs_DEMetro_Z |
4
|
-2.858
|
0.0101
|
-0.639
|
| DEMetro_Z_vs_SMC |
0
|
-6.397
|
3.91e-06
|
-1.430
|
| DEMetro_Z_vs_SMC |
1
|
6.110
|
7.12e-06
|
1.366
|
| DEMetro_Z_vs_SMC |
2
|
7.800
|
2.43e-07
|
1.744
|
| DEMetro_Z_vs_SMC |
3
|
7.629
|
3.37e-07
|
1.706
|
| DEMetro_Z_vs_SMC |
4
|
7.766
|
2.6e-07
|
1.737
|
| HMC_vs_DEMetro_Z |
0
|
-6.609
|
2.52e-06
|
-1.478
|
| HMC_vs_DEMetro_Z |
1
|
-4.781
|
0.00013
|
-1.069
|
| HMC_vs_DEMetro_Z |
2
|
-7.328
|
6.02e-07
|
-1.639
|
| HMC_vs_DEMetro_Z |
3
|
-5.996
|
9.05e-06
|
-1.341
|
| HMC_vs_DEMetro_Z |
4
|
-7.224
|
7.37e-07
|
-1.615
|
| HMC_vs_Metro |
0
|
-0.693
|
0.497
|
-0.155
|
| HMC_vs_Metro |
1
|
-3.460
|
0.00262
|
-0.774
|
| HMC_vs_Metro |
2
|
-5.545
|
2.39e-05
|
-1.240
|
| HMC_vs_Metro |
3
|
-5.792
|
1.4e-05
|
-1.295
|
| HMC_vs_Metro |
4
|
-5.206
|
5.03e-05
|
-1.164
|
| HMC_vs_SMC |
0
|
-7.857
|
2.19e-07
|
-1.757
|
| HMC_vs_SMC |
1
|
0.559
|
0.583
|
0.125
|
| HMC_vs_SMC |
2
|
1.735
|
0.0989
|
0.388
|
| HMC_vs_SMC |
3
|
1.634
|
0.119
|
0.365
|
| HMC_vs_SMC |
4
|
0.931
|
0.364
|
0.208
|
| Metro_vs_SMC |
0
|
-8.079
|
1.45e-07
|
-1.806
|
| Metro_vs_SMC |
1
|
4.701
|
0.000155
|
1.051
|
| Metro_vs_SMC |
2
|
5.132
|
5.92e-05
|
1.148
|
| Metro_vs_SMC |
3
|
10.568
|
2.15e-09
|
2.363
|
| Metro_vs_SMC |
4
|
5.574
|
2.24e-05
|
1.246
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.170 |
0.124 |
0.038 |
1.224 |
| HMC |
3.0 |
0.085 |
0.071 |
0.013 |
1.075 |
| HMC |
4.0 |
0.056 |
0.050 |
0.007 |
0.791 |
| HMC |
10.0 |
0.037 |
0.037 |
0.009 |
0.015 |
| HMC |
50.0 |
0.030 |
0.032 |
0.009 |
-0.220 |
| SMC |
2.1 |
0.897 |
0.124 |
0.038 |
20.527 |
| SMC |
3.0 |
0.080 |
0.071 |
0.013 |
0.680 |
| SMC |
4.0 |
0.050 |
0.050 |
0.007 |
0.094 |
| SMC |
10.0 |
0.033 |
0.037 |
0.009 |
-0.411 |
| SMC |
50.0 |
0.028 |
0.032 |
0.009 |
-0.402 |
| Metro |
2.1 |
0.185 |
0.124 |
0.038 |
1.610 |
| Metro |
3.0 |
0.122 |
0.071 |
0.013 |
4.007 |
| Metro |
4.0 |
0.086 |
0.050 |
0.007 |
4.966 |
| Metro |
10.0 |
0.054 |
0.037 |
0.009 |
1.833 |
| Metro |
50.0 |
0.044 |
0.032 |
0.009 |
1.318 |
| DEMetro_Z |
2.1 |
0.280 |
0.124 |
0.038 |
4.132 |
| DEMetro_Z |
3.0 |
0.148 |
0.071 |
0.013 |
6.043 |
| DEMetro_Z |
4.0 |
0.099 |
0.050 |
0.007 |
6.787 |
| DEMetro_Z |
10.0 |
0.070 |
0.037 |
0.009 |
3.477 |
| DEMetro_Z |
50.0 |
0.054 |
0.032 |
0.009 |
2.493 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.792 |
0.088 |
2.174 |
| HMC |
3.0 |
1.505 |
0.145 |
0.920 |
| HMC |
4.0 |
1.305 |
0.201 |
0.576 |
| HMC |
10.0 |
0.200 |
0.842 |
0.066 |
| HMC |
50.0 |
-0.298 |
0.767 |
-0.087 |
| SMC |
2.1 |
11.925 |
2.39e-10 |
30.700 |
| SMC |
3.0 |
2.525 |
0.0181 |
1.456 |
| SMC |
4.0 |
-0.002 |
0.999 |
-0.001 |
| SMC |
10.0 |
-1.114 |
0.273 |
-0.314 |
| SMC |
50.0 |
-1.363 |
0.181 |
-0.384 |
| Metro |
2.1 |
5.445 |
1.27e-05 |
3.410 |
| Metro |
3.0 |
6.566 |
5.86e-07 |
3.679 |
| Metro |
4.0 |
5.201 |
2.18e-05 |
3.085 |
| Metro |
10.0 |
4.136 |
0.000196 |
1.435 |
| Metro |
50.0 |
2.656 |
0.0118 |
0.982 |
| DEMetro_Z |
2.1 |
9.830 |
3.88e-10 |
5.724 |
| DEMetro_Z |
3.0 |
6.491 |
1.56e-06 |
5.323 |
| DEMetro_Z |
4.0 |
5.884 |
5.87e-06 |
4.532 |
| DEMetro_Z |
10.0 |
4.891 |
4.09e-05 |
2.574 |
| DEMetro_Z |
50.0 |
4.428 |
0.000122 |
2.078 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-9.502
|
1.19e-08
|
-2.125
|
| DEMetro_Z_vs_SMC |
1
|
3.963
|
0.000834
|
0.886
|
| DEMetro_Z_vs_SMC |
2
|
5.353
|
3.64e-05
|
1.197
|
| DEMetro_Z_vs_SMC |
3
|
5.915
|
1.08e-05
|
1.323
|
| DEMetro_Z_vs_SMC |
4
|
6.017
|
8.66e-06
|
1.345
|
| HMC_vs_Metro |
0
|
-0.955
|
0.351
|
-0.214
|
| HMC_vs_Metro |
1
|
-3.645
|
0.00172
|
-0.815
|
| HMC_vs_Metro |
2
|
-3.770
|
0.0013
|
-0.843
|
| HMC_vs_Metro |
3
|
-3.790
|
0.00124
|
-0.847
|
| HMC_vs_Metro |
4
|
-3.272
|
0.00401
|
-0.732
|
| Metro_vs_DEMetro_Z |
0
|
-3.501
|
0.00239
|
-0.783
|
| Metro_vs_DEMetro_Z |
1
|
-1.624
|
0.121
|
-0.363
|
| Metro_vs_DEMetro_Z |
2
|
-1.702
|
0.105
|
-0.381
|
| Metro_vs_DEMetro_Z |
3
|
-2.271
|
0.035
|
-0.508
|
| Metro_vs_DEMetro_Z |
4
|
-2.146
|
0.045
|
-0.480
|
| HMC_vs_SMC |
0
|
-8.823
|
3.8e-08
|
-1.973
|
| HMC_vs_SMC |
1
|
-0.625
|
0.539
|
-0.140
|
| HMC_vs_SMC |
2
|
1.388
|
0.181
|
0.310
|
| HMC_vs_SMC |
3
|
1.271
|
0.219
|
0.284
|
| HMC_vs_SMC |
4
|
1.177
|
0.254
|
0.263
|
| Metro_vs_SMC |
0
|
-10.659
|
1.87e-09
|
-2.383
|
| Metro_vs_SMC |
1
|
3.205
|
0.00466
|
0.717
|
| Metro_vs_SMC |
2
|
4.563
|
0.000212
|
1.020
|
| Metro_vs_SMC |
3
|
6.031
|
8.41e-06
|
1.348
|
| Metro_vs_SMC |
4
|
4.302
|
0.000385
|
0.962
|
| HMC_vs_DEMetro_Z |
0
|
-2.684
|
0.0147
|
-0.600
|
| HMC_vs_DEMetro_Z |
1
|
-4.033
|
0.000711
|
-0.902
|
| HMC_vs_DEMetro_Z |
2
|
-4.832
|
0.000116
|
-1.081
|
| HMC_vs_DEMetro_Z |
3
|
-4.281
|
0.000404
|
-0.957
|
| HMC_vs_DEMetro_Z |
4
|
-4.955
|
8.8e-05
|
-1.108
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.025 |
0.014 |
0.005 |
2.174 |
| HMC |
3.0 |
0.018 |
0.015 |
0.003 |
0.920 |
| HMC |
4.0 |
0.017 |
0.015 |
0.003 |
0.576 |
| HMC |
10.0 |
0.015 |
0.015 |
0.005 |
0.066 |
| HMC |
50.0 |
0.014 |
0.015 |
0.005 |
-0.087 |
| SMC |
2.1 |
0.158 |
0.014 |
0.005 |
30.700 |
| SMC |
3.0 |
0.020 |
0.015 |
0.003 |
1.456 |
| SMC |
4.0 |
0.015 |
0.015 |
0.003 |
-0.001 |
| SMC |
10.0 |
0.013 |
0.015 |
0.005 |
-0.314 |
| SMC |
50.0 |
0.013 |
0.015 |
0.005 |
-0.384 |
| Metro |
2.1 |
0.030 |
0.014 |
0.005 |
3.410 |
| Metro |
3.0 |
0.028 |
0.015 |
0.003 |
3.679 |
| Metro |
4.0 |
0.025 |
0.015 |
0.003 |
3.085 |
| Metro |
10.0 |
0.023 |
0.015 |
0.005 |
1.435 |
| Metro |
50.0 |
0.020 |
0.015 |
0.005 |
0.982 |
| DEMetro_Z |
2.1 |
0.041 |
0.014 |
0.005 |
5.724 |
| DEMetro_Z |
3.0 |
0.033 |
0.015 |
0.003 |
5.323 |
| DEMetro_Z |
4.0 |
0.030 |
0.015 |
0.003 |
4.532 |
| DEMetro_Z |
10.0 |
0.029 |
0.015 |
0.005 |
2.574 |
| DEMetro_Z |
50.0 |
0.026 |
0.015 |
0.005 |
2.078 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.680 |
0.104 |
-0.420 |
| HMC |
3.0 |
-0.653 |
0.518 |
-0.176 |
| HMC |
4.0 |
0.481 |
0.633 |
0.146 |
| HMC |
10.0 |
-0.399 |
0.692 |
-0.119 |
| HMC |
50.0 |
-1.537 |
0.133 |
-0.429 |
| SMC |
2.1 |
1.228 |
0.227 |
0.431 |
| SMC |
3.0 |
0.047 |
0.963 |
0.013 |
| SMC |
4.0 |
1.094 |
0.281 |
0.401 |
| SMC |
10.0 |
-0.083 |
0.935 |
-0.022 |
| SMC |
50.0 |
-0.940 |
0.353 |
-0.276 |
| Metro |
2.1 |
3.353 |
0.00228 |
1.649 |
| Metro |
3.0 |
3.807 |
0.00058 |
1.539 |
| Metro |
4.0 |
3.009 |
0.00584 |
1.738 |
| Metro |
10.0 |
3.024 |
0.00486 |
1.260 |
| Metro |
50.0 |
1.304 |
0.201 |
0.479 |
| DEMetro_Z |
2.1 |
4.032 |
0.000312 |
1.655 |
| DEMetro_Z |
3.0 |
2.834 |
0.00818 |
1.305 |
| DEMetro_Z |
4.0 |
3.431 |
0.00244 |
3.046 |
| DEMetro_Z |
10.0 |
3.625 |
0.000928 |
1.400 |
| DEMetro_Z |
50.0 |
3.589 |
0.00119 |
1.680 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-5.279
|
4.28e-05
|
-1.180
|
| HMC_vs_DEMetro_Z |
1
|
-3.289
|
0.00386
|
-0.735
|
| HMC_vs_DEMetro_Z |
2
|
-3.254
|
0.00417
|
-0.728
|
| HMC_vs_DEMetro_Z |
3
|
-4.879
|
0.000104
|
-1.091
|
| HMC_vs_DEMetro_Z |
4
|
-5.055
|
7.04e-05
|
-1.130
|
| Metro_vs_SMC |
0
|
2.386
|
0.0276
|
0.534
|
| Metro_vs_SMC |
1
|
4.363
|
0.000335
|
0.976
|
| Metro_vs_SMC |
2
|
2.317
|
0.0318
|
0.518
|
| Metro_vs_SMC |
3
|
3.732
|
0.00141
|
0.834
|
| Metro_vs_SMC |
4
|
2.346
|
0.03
|
0.525
|
| Metro_vs_DEMetro_Z |
0
|
-0.012
|
0.991
|
-0.003
|
| Metro_vs_DEMetro_Z |
1
|
0.476
|
0.64
|
0.106
|
| Metro_vs_DEMetro_Z |
2
|
-1.174
|
0.255
|
-0.263
|
| Metro_vs_DEMetro_Z |
3
|
-0.322
|
0.751
|
-0.072
|
| Metro_vs_DEMetro_Z |
4
|
-3.706
|
0.0015
|
-0.829
|
| HMC_vs_Metro |
0
|
-4.687
|
0.00016
|
-1.048
|
| HMC_vs_Metro |
1
|
-5.410
|
3.21e-05
|
-1.210
|
| HMC_vs_Metro |
2
|
-3.174
|
0.005
|
-0.710
|
| HMC_vs_Metro |
3
|
-3.638
|
0.00175
|
-0.813
|
| HMC_vs_Metro |
4
|
-2.766
|
0.0123
|
-0.619
|
| HMC_vs_SMC |
0
|
-2.902
|
0.00914
|
-0.649
|
| HMC_vs_SMC |
1
|
-1.111
|
0.28
|
-0.248
|
| HMC_vs_SMC |
2
|
-0.741
|
0.468
|
-0.166
|
| HMC_vs_SMC |
3
|
-0.390
|
0.701
|
-0.087
|
| HMC_vs_SMC |
4
|
-0.654
|
0.521
|
-0.146
|
| DEMetro_Z_vs_SMC |
0
|
2.847
|
0.0103
|
0.637
|
| DEMetro_Z_vs_SMC |
1
|
2.850
|
0.0103
|
0.637
|
| DEMetro_Z_vs_SMC |
2
|
3.121
|
0.00562
|
0.698
|
| DEMetro_Z_vs_SMC |
3
|
4.228
|
0.000455
|
0.945
|
| DEMetro_Z_vs_SMC |
4
|
4.573
|
0.000208
|
1.023
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.050 |
0.066 |
0.039 |
-0.420 |
| HMC |
3.0 |
0.035 |
0.039 |
0.023 |
-0.176 |
| HMC |
4.0 |
0.030 |
0.028 |
0.014 |
0.146 |
| HMC |
10.0 |
0.025 |
0.026 |
0.015 |
-0.119 |
| HMC |
50.0 |
0.018 |
0.024 |
0.013 |
-0.429 |
| SMC |
2.1 |
0.083 |
0.066 |
0.039 |
0.431 |
| SMC |
3.0 |
0.040 |
0.039 |
0.023 |
0.013 |
| SMC |
4.0 |
0.033 |
0.028 |
0.014 |
0.401 |
| SMC |
10.0 |
0.026 |
0.026 |
0.015 |
-0.022 |
| SMC |
50.0 |
0.020 |
0.024 |
0.013 |
-0.276 |
| Metro |
2.1 |
0.131 |
0.066 |
0.039 |
1.649 |
| Metro |
3.0 |
0.075 |
0.039 |
0.023 |
1.539 |
| Metro |
4.0 |
0.052 |
0.028 |
0.014 |
1.738 |
| Metro |
10.0 |
0.045 |
0.026 |
0.015 |
1.260 |
| Metro |
50.0 |
0.030 |
0.024 |
0.013 |
0.479 |
| DEMetro_Z |
2.1 |
0.131 |
0.066 |
0.039 |
1.655 |
| DEMetro_Z |
3.0 |
0.070 |
0.039 |
0.023 |
1.305 |
| DEMetro_Z |
4.0 |
0.070 |
0.028 |
0.014 |
3.046 |
| DEMetro_Z |
10.0 |
0.047 |
0.026 |
0.015 |
1.400 |
| DEMetro_Z |
50.0 |
0.045 |
0.024 |
0.013 |
1.680 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.809 |
0.425 |
-0.214 |
| HMC |
3.0 |
0.061 |
0.952 |
0.019 |
| HMC |
4.0 |
0.362 |
0.72 |
0.120 |
| HMC |
10.0 |
0.048 |
0.962 |
0.017 |
| HMC |
50.0 |
1.061 |
0.296 |
0.368 |
| SMC |
2.1 |
-0.168 |
0.868 |
-0.044 |
| SMC |
3.0 |
-0.400 |
0.692 |
-0.118 |
| SMC |
4.0 |
-1.175 |
0.25 |
-0.294 |
| SMC |
10.0 |
0.381 |
0.705 |
0.139 |
| SMC |
50.0 |
-0.699 |
0.49 |
-0.184 |
| Metro |
2.1 |
-0.718 |
0.478 |
-0.188 |
| Metro |
3.0 |
1.564 |
0.126 |
0.553 |
| Metro |
4.0 |
1.972 |
0.0561 |
0.675 |
| Metro |
10.0 |
3.741 |
0.000875 |
1.967 |
| Metro |
50.0 |
3.520 |
0.00118 |
1.260 |
| DEMetro_Z |
2.1 |
-0.635 |
0.529 |
-0.171 |
| DEMetro_Z |
3.0 |
1.188 |
0.243 |
0.346 |
| DEMetro_Z |
4.0 |
1.917 |
0.0691 |
2.003 |
| DEMetro_Z |
10.0 |
4.691 |
7.98e-05 |
2.722 |
| DEMetro_Z |
50.0 |
4.054 |
0.000342 |
1.906 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-2.278
|
0.0344
|
-0.509
|
| HMC_vs_SMC |
1
|
0.763
|
0.455
|
0.171
|
| HMC_vs_SMC |
2
|
1.591
|
0.128
|
0.356
|
| HMC_vs_SMC |
3
|
-0.324
|
0.749
|
-0.073
|
| HMC_vs_SMC |
4
|
1.967
|
0.064
|
0.440
|
| Metro_vs_DEMetro_Z |
0
|
-0.547
|
0.59
|
-0.122
|
| Metro_vs_DEMetro_Z |
1
|
0.900
|
0.379
|
0.201
|
| Metro_vs_DEMetro_Z |
2
|
-1.234
|
0.232
|
-0.276
|
| Metro_vs_DEMetro_Z |
3
|
-1.017
|
0.322
|
-0.227
|
| Metro_vs_DEMetro_Z |
4
|
-1.455
|
0.162
|
-0.325
|
| HMC_vs_Metro |
0
|
-0.704
|
0.49
|
-0.157
|
| HMC_vs_Metro |
1
|
-3.032
|
0.00686
|
-0.678
|
| HMC_vs_Metro |
2
|
-1.556
|
0.136
|
-0.348
|
| HMC_vs_Metro |
3
|
-3.409
|
0.00294
|
-0.762
|
| HMC_vs_Metro |
4
|
-2.109
|
0.0484
|
-0.472
|
| HMC_vs_DEMetro_Z |
0
|
-1.355
|
0.191
|
-0.303
|
| HMC_vs_DEMetro_Z |
1
|
-1.703
|
0.105
|
-0.381
|
| HMC_vs_DEMetro_Z |
2
|
-1.739
|
0.0983
|
-0.389
|
| HMC_vs_DEMetro_Z |
3
|
-5.017
|
7.65e-05
|
-1.122
|
| HMC_vs_DEMetro_Z |
4
|
-2.746
|
0.0128
|
-0.614
|
| Metro_vs_SMC |
0
|
-2.178
|
0.0422
|
-0.487
|
| Metro_vs_SMC |
1
|
3.136
|
0.00544
|
0.701
|
| Metro_vs_SMC |
2
|
4.915
|
9.61e-05
|
1.099
|
| Metro_vs_SMC |
3
|
3.101
|
0.00588
|
0.694
|
| Metro_vs_SMC |
4
|
4.032
|
0.000713
|
0.902
|
| DEMetro_Z_vs_SMC |
0
|
-1.587
|
0.129
|
-0.355
|
| DEMetro_Z_vs_SMC |
1
|
2.449
|
0.0242
|
0.548
|
| DEMetro_Z_vs_SMC |
2
|
2.249
|
0.0366
|
0.503
|
| DEMetro_Z_vs_SMC |
3
|
3.654
|
0.00169
|
0.817
|
| DEMetro_Z_vs_SMC |
4
|
4.616
|
0.000188
|
1.032
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.041 |
9.309 |
15.244 |
-0.214 |
| HMC |
3.0 |
0.560 |
0.552 |
0.433 |
0.019 |
| HMC |
4.0 |
0.190 |
0.173 |
0.139 |
0.120 |
| HMC |
10.0 |
0.040 |
0.040 |
0.020 |
0.017 |
| HMC |
50.0 |
0.038 |
0.031 |
0.019 |
0.368 |
| SMC |
2.1 |
8.644 |
9.309 |
15.244 |
-0.044 |
| SMC |
3.0 |
0.501 |
0.552 |
0.433 |
-0.118 |
| SMC |
4.0 |
0.132 |
0.173 |
0.139 |
-0.294 |
| SMC |
10.0 |
0.043 |
0.040 |
0.020 |
0.139 |
| SMC |
50.0 |
0.028 |
0.031 |
0.019 |
-0.184 |
| Metro |
2.1 |
6.440 |
9.309 |
15.244 |
-0.188 |
| Metro |
3.0 |
0.792 |
0.552 |
0.433 |
0.553 |
| Metro |
4.0 |
0.267 |
0.173 |
0.139 |
0.675 |
| Metro |
10.0 |
0.080 |
0.040 |
0.020 |
1.967 |
| Metro |
50.0 |
0.055 |
0.031 |
0.019 |
1.260 |
| DEMetro_Z |
2.1 |
6.701 |
9.309 |
15.244 |
-0.171 |
| DEMetro_Z |
3.0 |
0.702 |
0.552 |
0.433 |
0.346 |
| DEMetro_Z |
4.0 |
0.451 |
0.173 |
0.139 |
2.003 |
| DEMetro_Z |
10.0 |
0.095 |
0.040 |
0.020 |
2.722 |
| DEMetro_Z |
50.0 |
0.067 |
0.031 |
0.019 |
1.906 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.159 |
0.254 |
0.420 |
| HMC |
3.0 |
0.876 |
0.388 |
0.364 |
| HMC |
4.0 |
1.045 |
0.304 |
0.436 |
| HMC |
10.0 |
0.147 |
0.884 |
0.044 |
| HMC |
50.0 |
-0.560 |
0.579 |
-0.154 |
| SMC |
2.1 |
6.905 |
1.05e-06 |
9.675 |
| SMC |
3.0 |
0.542 |
0.592 |
0.223 |
| SMC |
4.0 |
0.180 |
0.858 |
0.063 |
| SMC |
10.0 |
-0.344 |
0.733 |
-0.100 |
| SMC |
50.0 |
-1.110 |
0.275 |
-0.306 |
| Metro |
2.1 |
7.308 |
3.57e-08 |
3.267 |
| Metro |
3.0 |
7.687 |
4.04e-08 |
4.387 |
| Metro |
4.0 |
6.728 |
6.76e-07 |
4.668 |
| Metro |
10.0 |
5.387 |
8.28e-06 |
2.511 |
| Metro |
50.0 |
4.378 |
9.09e-05 |
1.408 |
| DEMetro_Z |
2.1 |
9.746 |
1.25e-11 |
3.535 |
| DEMetro_Z |
3.0 |
7.915 |
2.13e-08 |
4.403 |
| DEMetro_Z |
4.0 |
6.275 |
3.76e-06 |
7.838 |
| DEMetro_Z |
10.0 |
6.875 |
1.08e-07 |
3.025 |
| DEMetro_Z |
50.0 |
6.077 |
1.33e-06 |
2.914 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.657
|
0.519
|
-0.147
|
| Metro_vs_DEMetro_Z |
1
|
-0.028
|
0.978
|
-0.006
|
| Metro_vs_DEMetro_Z |
2
|
-2.009
|
0.059
|
-0.449
|
| Metro_vs_DEMetro_Z |
3
|
-0.970
|
0.344
|
-0.217
|
| Metro_vs_DEMetro_Z |
4
|
-4.604
|
0.000194
|
-1.029
|
| DEMetro_Z_vs_SMC |
0
|
-4.044
|
0.000693
|
-0.904
|
| DEMetro_Z_vs_SMC |
1
|
7.685
|
3.03e-07
|
1.719
|
| DEMetro_Z_vs_SMC |
2
|
6.682
|
2.17e-06
|
1.494
|
| DEMetro_Z_vs_SMC |
3
|
8.435
|
7.56e-08
|
1.886
|
| DEMetro_Z_vs_SMC |
4
|
7.377
|
5.47e-07
|
1.650
|
| HMC_vs_DEMetro_Z |
0
|
-11.854
|
3.19e-10
|
-2.651
|
| HMC_vs_DEMetro_Z |
1
|
-5.835
|
1.28e-05
|
-1.305
|
| HMC_vs_DEMetro_Z |
2
|
-5.370
|
3.5e-05
|
-1.201
|
| HMC_vs_DEMetro_Z |
3
|
-8.953
|
3.03e-08
|
-2.002
|
| HMC_vs_DEMetro_Z |
4
|
-6.282
|
4.96e-06
|
-1.405
|
| HMC_vs_Metro |
0
|
-6.477
|
3.31e-06
|
-1.448
|
| HMC_vs_Metro |
1
|
-6.692
|
2.13e-06
|
-1.496
|
| HMC_vs_Metro |
2
|
-5.980
|
9.37e-06
|
-1.337
|
| HMC_vs_Metro |
3
|
-5.372
|
3.49e-05
|
-1.201
|
| HMC_vs_Metro |
4
|
-4.868
|
0.000107
|
-1.088
|
| HMC_vs_SMC |
0
|
-6.294
|
4.84e-06
|
-1.407
|
| HMC_vs_SMC |
1
|
0.387
|
0.703
|
0.087
|
| HMC_vs_SMC |
2
|
0.892
|
0.384
|
0.199
|
| HMC_vs_SMC |
3
|
0.520
|
0.609
|
0.116
|
| HMC_vs_SMC |
4
|
0.599
|
0.556
|
0.134
|
| Metro_vs_SMC |
0
|
-4.600
|
0.000195
|
-1.029
|
| Metro_vs_SMC |
1
|
6.754
|
1.88e-06
|
1.510
|
| Metro_vs_SMC |
2
|
6.260
|
5.19e-06
|
1.400
|
| Metro_vs_SMC |
3
|
6.270
|
5.09e-06
|
1.402
|
| Metro_vs_SMC |
4
|
7.079
|
9.8e-07
|
1.583
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.140 |
0.124 |
0.038 |
0.420 |
| HMC |
3.0 |
0.076 |
0.071 |
0.013 |
0.364 |
| HMC |
4.0 |
0.053 |
0.050 |
0.007 |
0.436 |
| HMC |
10.0 |
0.037 |
0.037 |
0.009 |
0.044 |
| HMC |
50.0 |
0.030 |
0.032 |
0.009 |
-0.154 |
| SMC |
2.1 |
0.488 |
0.124 |
0.038 |
9.675 |
| SMC |
3.0 |
0.074 |
0.071 |
0.013 |
0.223 |
| SMC |
4.0 |
0.050 |
0.050 |
0.007 |
0.063 |
| SMC |
10.0 |
0.036 |
0.037 |
0.009 |
-0.100 |
| SMC |
50.0 |
0.029 |
0.032 |
0.009 |
-0.306 |
| Metro |
2.1 |
0.247 |
0.124 |
0.038 |
3.267 |
| Metro |
3.0 |
0.127 |
0.071 |
0.013 |
4.387 |
| Metro |
4.0 |
0.084 |
0.050 |
0.007 |
4.668 |
| Metro |
10.0 |
0.061 |
0.037 |
0.009 |
2.511 |
| Metro |
50.0 |
0.044 |
0.032 |
0.009 |
1.408 |
| DEMetro_Z |
2.1 |
0.257 |
0.124 |
0.038 |
3.535 |
| DEMetro_Z |
3.0 |
0.127 |
0.071 |
0.013 |
4.403 |
| DEMetro_Z |
4.0 |
0.107 |
0.050 |
0.007 |
7.838 |
| DEMetro_Z |
10.0 |
0.066 |
0.037 |
0.009 |
3.025 |
| DEMetro_Z |
50.0 |
0.058 |
0.032 |
0.009 |
2.914 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.373 |
0.0233 |
0.907 |
| HMC |
3.0 |
1.255 |
0.219 |
0.537 |
| HMC |
4.0 |
-0.656 |
0.516 |
-0.244 |
| HMC |
10.0 |
0.887 |
0.381 |
0.281 |
| HMC |
50.0 |
-0.025 |
0.98 |
-0.007 |
| SMC |
2.1 |
9.088 |
1.97e-08 |
18.929 |
| SMC |
3.0 |
1.290 |
0.209 |
0.768 |
| SMC |
4.0 |
-0.612 |
0.544 |
-0.193 |
| SMC |
10.0 |
0.058 |
0.954 |
0.018 |
| SMC |
50.0 |
-0.610 |
0.546 |
-0.173 |
| Metro |
2.1 |
9.865 |
8.4e-11 |
4.648 |
| Metro |
3.0 |
6.839 |
5.1e-07 |
4.697 |
| Metro |
4.0 |
6.821 |
2.14e-07 |
3.430 |
| Metro |
10.0 |
4.816 |
4.34e-05 |
2.320 |
| Metro |
50.0 |
4.081 |
0.000222 |
1.283 |
| DEMetro_Z |
2.1 |
7.608 |
9.15e-08 |
5.286 |
| DEMetro_Z |
3.0 |
6.893 |
3.89e-07 |
4.449 |
| DEMetro_Z |
4.0 |
7.801 |
4.1e-08 |
4.805 |
| DEMetro_Z |
10.0 |
5.143 |
1.69e-05 |
2.431 |
| DEMetro_Z |
50.0 |
4.733 |
5.36e-05 |
2.258 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-6.050
|
8.08e-06
|
-1.353
|
| DEMetro_Z_vs_SMC |
1
|
4.983
|
8.25e-05
|
1.114
|
| DEMetro_Z_vs_SMC |
2
|
7.663
|
3.16e-07
|
1.714
|
| DEMetro_Z_vs_SMC |
3
|
6.434
|
3.61e-06
|
1.439
|
| DEMetro_Z_vs_SMC |
4
|
5.422
|
3.12e-05
|
1.212
|
| HMC_vs_Metro |
0
|
-6.330
|
4.49e-06
|
-1.415
|
| HMC_vs_Metro |
1
|
-6.762
|
1.85e-06
|
-1.512
|
| HMC_vs_Metro |
2
|
-6.999
|
1.15e-06
|
-1.565
|
| HMC_vs_Metro |
3
|
-4.163
|
0.000528
|
-0.931
|
| HMC_vs_Metro |
4
|
-3.777
|
0.00127
|
-0.845
|
| Metro_vs_DEMetro_Z |
0
|
-0.875
|
0.392
|
-0.196
|
| Metro_vs_DEMetro_Z |
1
|
0.276
|
0.786
|
0.062
|
| Metro_vs_DEMetro_Z |
2
|
-1.605
|
0.125
|
-0.359
|
| Metro_vs_DEMetro_Z |
3
|
-0.199
|
0.845
|
-0.044
|
| Metro_vs_DEMetro_Z |
4
|
-2.817
|
0.011
|
-0.630
|
| HMC_vs_SMC |
0
|
-8.826
|
3.78e-08
|
-1.973
|
| HMC_vs_SMC |
1
|
-0.371
|
0.715
|
-0.083
|
| HMC_vs_SMC |
2
|
-0.136
|
0.893
|
-0.030
|
| HMC_vs_SMC |
3
|
0.919
|
0.369
|
0.206
|
| HMC_vs_SMC |
4
|
0.558
|
0.583
|
0.125
|
| Metro_vs_SMC |
0
|
-7.225
|
7.35e-07
|
-1.616
|
| Metro_vs_SMC |
1
|
4.608
|
0.000192
|
1.030
|
| Metro_vs_SMC |
2
|
7.674
|
3.09e-07
|
1.716
|
| Metro_vs_SMC |
3
|
5.262
|
4.45e-05
|
1.177
|
| Metro_vs_SMC |
4
|
6.063
|
7.86e-06
|
1.356
|
| HMC_vs_DEMetro_Z |
0
|
-6.904
|
1.39e-06
|
-1.544
|
| HMC_vs_DEMetro_Z |
1
|
-5.490
|
2.7e-05
|
-1.228
|
| HMC_vs_DEMetro_Z |
2
|
-6.644
|
2.35e-06
|
-1.486
|
| HMC_vs_DEMetro_Z |
3
|
-5.573
|
2.25e-05
|
-1.246
|
| HMC_vs_DEMetro_Z |
4
|
-4.480
|
0.000257
|
-1.002
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.019 |
0.014 |
0.005 |
0.907 |
| HMC |
3.0 |
0.017 |
0.015 |
0.003 |
0.537 |
| HMC |
4.0 |
0.014 |
0.015 |
0.003 |
-0.244 |
| HMC |
10.0 |
0.016 |
0.015 |
0.005 |
0.281 |
| HMC |
50.0 |
0.015 |
0.015 |
0.005 |
-0.007 |
| SMC |
2.1 |
0.103 |
0.014 |
0.005 |
18.929 |
| SMC |
3.0 |
0.018 |
0.015 |
0.003 |
0.768 |
| SMC |
4.0 |
0.014 |
0.015 |
0.003 |
-0.193 |
| SMC |
10.0 |
0.015 |
0.015 |
0.005 |
0.018 |
| SMC |
50.0 |
0.014 |
0.015 |
0.005 |
-0.173 |
| Metro |
2.1 |
0.036 |
0.014 |
0.005 |
4.648 |
| Metro |
3.0 |
0.031 |
0.015 |
0.003 |
4.697 |
| Metro |
4.0 |
0.026 |
0.015 |
0.003 |
3.430 |
| Metro |
10.0 |
0.027 |
0.015 |
0.005 |
2.320 |
| Metro |
50.0 |
0.022 |
0.015 |
0.005 |
1.283 |
| DEMetro_Z |
2.1 |
0.039 |
0.014 |
0.005 |
5.286 |
| DEMetro_Z |
3.0 |
0.030 |
0.015 |
0.003 |
4.449 |
| DEMetro_Z |
4.0 |
0.031 |
0.015 |
0.003 |
4.805 |
| DEMetro_Z |
10.0 |
0.028 |
0.015 |
0.005 |
2.431 |
| DEMetro_Z |
50.0 |
0.027 |
0.015 |
0.005 |
2.258 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Dimension
(MvStudentT,
nu,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.543 |
0.139 |
5.596 |
| HMC |
3.0 |
2.107 |
0.0486 |
10.613 |
| HMC |
4.0 |
0.384 |
0.704 |
0.285 |
| HMC |
10.0 |
-1.924 |
0.0626 |
-0.530 |
| HMC |
50.0 |
-3.176 |
0.00309 |
-0.890 |
| SMC |
2.1 |
32.386 |
2.31e-18 |
70.188 |
| SMC |
3.0 |
31.204 |
7.07e-18 |
116.418 |
| SMC |
4.0 |
29.005 |
2.44e-17 |
84.083 |
| SMC |
10.0 |
24.766 |
3.36e-16 |
48.880 |
| SMC |
50.0 |
21.251 |
6.14e-16 |
18.941 |
| Metro |
2.1 |
4.122 |
0.000571 |
13.866 |
| Metro |
3.0 |
11.409 |
1.8e-10 |
11.291 |
| Metro |
4.0 |
16.730 |
2.94e-15 |
9.671 |
| Metro |
10.0 |
15.079 |
2.3e-15 |
7.046 |
| Metro |
50.0 |
14.552 |
5.3e-16 |
5.815 |
| DEMetro_Z |
2.1 |
17.660 |
3e-13 |
335.130 |
| DEMetro_Z |
3.0 |
20.961 |
1.35e-14 |
620.466 |
| DEMetro_Z |
4.0 |
16.329 |
1.22e-12 |
473.692 |
| DEMetro_Z |
10.0 |
23.729 |
1.36e-15 |
243.476 |
| DEMetro_Z |
50.0 |
11.683 |
4.06e-10 |
288.577 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-16.661
|
8.56e-13
|
-3.726
|
| HMC_vs_DEMetro_Z |
1
|
-20.612
|
1.84e-14
|
-4.609
|
| HMC_vs_DEMetro_Z |
2
|
-16.218
|
1.38e-12
|
-3.626
|
| HMC_vs_DEMetro_Z |
3
|
-23.693
|
1.43e-15
|
-5.298
|
| HMC_vs_DEMetro_Z |
4
|
-11.712
|
3.9e-10
|
-2.619
|
| Metro_vs_SMC |
0
|
-14.427
|
1.09e-11
|
-3.226
|
| Metro_vs_SMC |
1
|
-26.492
|
1.82e-16
|
-5.924
|
| Metro_vs_SMC |
2
|
-25.728
|
3.13e-16
|
-5.753
|
| Metro_vs_SMC |
3
|
-21.373
|
9.5e-15
|
-4.779
|
| Metro_vs_SMC |
4
|
-14.869
|
6.42e-12
|
-3.325
|
| Metro_vs_DEMetro_Z |
0
|
-16.466
|
1.06e-12
|
-3.682
|
| Metro_vs_DEMetro_Z |
1
|
-20.446
|
2.13e-14
|
-4.572
|
| Metro_vs_DEMetro_Z |
2
|
-16.035
|
1.69e-12
|
-3.586
|
| Metro_vs_DEMetro_Z |
3
|
-22.922
|
2.63e-15
|
-5.126
|
| Metro_vs_DEMetro_Z |
4
|
-11.458
|
5.63e-10
|
-2.562
|
| HMC_vs_Metro |
0
|
-1.571
|
0.133
|
-0.351
|
| HMC_vs_Metro |
1
|
-0.134
|
0.895
|
-0.030
|
| HMC_vs_Metro |
2
|
-11.130
|
9.14e-10
|
-2.489
|
| HMC_vs_Metro |
3
|
-15.918
|
1.93e-12
|
-3.559
|
| HMC_vs_Metro |
4
|
-16.223
|
1.38e-12
|
-3.628
|
| HMC_vs_SMC |
0
|
-18.241
|
1.69e-13
|
-4.079
|
| HMC_vs_SMC |
1
|
-17.115
|
5.3e-13
|
-3.827
|
| HMC_vs_SMC |
2
|
-25.181
|
4.66e-16
|
-5.631
|
| HMC_vs_SMC |
3
|
-25.282
|
4.33e-16
|
-5.653
|
| HMC_vs_SMC |
4
|
-23.140
|
2.21e-15
|
-5.174
|
| DEMetro_Z_vs_SMC |
0
|
13.954
|
1.95e-11
|
3.120
|
| DEMetro_Z_vs_SMC |
1
|
17.262
|
4.55e-13
|
3.860
|
| DEMetro_Z_vs_SMC |
2
|
13.553
|
3.23e-11
|
3.031
|
| DEMetro_Z_vs_SMC |
3
|
18.241
|
1.69e-13
|
4.079
|
| DEMetro_Z_vs_SMC |
4
|
10.781
|
1.55e-09
|
2.411
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.191 |
0.068 |
0.022 |
5.596 |
| HMC |
3.0 |
0.080 |
0.036 |
0.004 |
10.613 |
| HMC |
4.0 |
0.033 |
0.032 |
0.003 |
0.285 |
| HMC |
10.0 |
0.022 |
0.024 |
0.004 |
-0.530 |
| HMC |
50.0 |
0.019 |
0.022 |
0.003 |
-0.890 |
| SMC |
2.1 |
1.612 |
0.068 |
0.022 |
70.188 |
| SMC |
3.0 |
0.521 |
0.036 |
0.004 |
116.418 |
| SMC |
4.0 |
0.320 |
0.032 |
0.003 |
84.083 |
| SMC |
10.0 |
0.203 |
0.024 |
0.004 |
48.880 |
| SMC |
50.0 |
0.083 |
0.022 |
0.003 |
18.941 |
| Metro |
2.1 |
0.373 |
0.068 |
0.022 |
13.866 |
| Metro |
3.0 |
0.083 |
0.036 |
0.004 |
11.291 |
| Metro |
4.0 |
0.065 |
0.032 |
0.003 |
9.671 |
| Metro |
10.0 |
0.050 |
0.024 |
0.004 |
7.046 |
| Metro |
50.0 |
0.041 |
0.022 |
0.003 |
5.815 |
| DEMetro_Z |
2.1 |
7.438 |
0.068 |
0.022 |
335.130 |
| DEMetro_Z |
3.0 |
2.619 |
0.036 |
0.004 |
620.466 |
| DEMetro_Z |
4.0 |
1.658 |
0.032 |
0.003 |
473.692 |
| DEMetro_Z |
10.0 |
0.916 |
0.024 |
0.004 |
243.476 |
| DEMetro_Z |
50.0 |
0.955 |
0.022 |
0.003 |
288.577 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.126 |
0.272 |
0.879 |
| HMC |
3.0 |
2.196 |
0.0348 |
0.822 |
| HMC |
4.0 |
2.710 |
0.0132 |
2.943 |
| HMC |
10.0 |
5.035 |
5.15e-05 |
4.510 |
| HMC |
50.0 |
7.131 |
4.55e-08 |
3.031 |
| SMC |
2.1 |
164.278 |
5.83e-34 |
169.471 |
| SMC |
3.0 |
126.843 |
2.42e-29 |
838.185 |
| SMC |
4.0 |
170.240 |
1.02e-31 |
3897.980 |
| SMC |
10.0 |
87.339 |
3.25e-26 |
15438.243 |
| SMC |
50.0 |
37.079 |
3.44e-19 |
1395.231 |
| Metro |
2.1 |
1.869 |
0.0766 |
3.343 |
| Metro |
3.0 |
2.628 |
0.0128 |
1.025 |
| Metro |
4.0 |
4.373 |
0.000292 |
5.900 |
| Metro |
10.0 |
11.569 |
1.41e-10 |
11.515 |
| Metro |
50.0 |
17.271 |
1.05e-17 |
7.319 |
| DEMetro_Z |
2.1 |
11.391 |
5.77e-10 |
45.665 |
| DEMetro_Z |
3.0 |
10.811 |
1.47e-09 |
181.266 |
| DEMetro_Z |
4.0 |
12.091 |
2.28e-10 |
797.399 |
| DEMetro_Z |
10.0 |
15.911 |
1.94e-12 |
1687.856 |
| DEMetro_Z |
50.0 |
6.439 |
3.58e-06 |
1859.398 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-148.273
|
1.42e-30
|
-33.155
|
| HMC_vs_SMC |
1
|
-124.376
|
3.98e-29
|
-27.811
|
| HMC_vs_SMC |
2
|
-168.781
|
1.21e-31
|
-37.741
|
| HMC_vs_SMC |
3
|
-87.315
|
3.27e-26
|
-19.524
|
| HMC_vs_SMC |
4
|
-37.019
|
3.56e-19
|
-8.278
|
| Metro_vs_DEMetro_Z |
0
|
-9.407
|
1.4e-08
|
-2.103
|
| Metro_vs_DEMetro_Z |
1
|
-10.822
|
1.45e-09
|
-2.420
|
| Metro_vs_DEMetro_Z |
2
|
-11.925
|
2.88e-10
|
-2.667
|
| Metro_vs_DEMetro_Z |
3
|
-15.781
|
2.25e-12
|
-3.529
|
| Metro_vs_DEMetro_Z |
4
|
-6.412
|
3.78e-06
|
-1.434
|
| HMC_vs_Metro |
0
|
-1.278
|
0.217
|
-0.286
|
| HMC_vs_Metro |
1
|
-0.658
|
0.519
|
-0.147
|
| HMC_vs_Metro |
2
|
-1.488
|
0.153
|
-0.333
|
| HMC_vs_Metro |
3
|
-5.260
|
4.47e-05
|
-1.176
|
| HMC_vs_Metro |
4
|
-8.480
|
6.98e-08
|
-1.896
|
| HMC_vs_DEMetro_Z |
0
|
-11.088
|
9.73e-10
|
-2.479
|
| HMC_vs_DEMetro_Z |
1
|
-10.784
|
1.54e-09
|
-2.411
|
| HMC_vs_DEMetro_Z |
2
|
-12.082
|
2.31e-10
|
-2.702
|
| HMC_vs_DEMetro_Z |
3
|
-15.888
|
1.99e-12
|
-3.553
|
| HMC_vs_DEMetro_Z |
4
|
-6.427
|
3.67e-06
|
-1.437
|
| Metro_vs_SMC |
0
|
-81.474
|
1.21e-25
|
-18.218
|
| Metro_vs_SMC |
1
|
-126.671
|
2.82e-29
|
-28.324
|
| Metro_vs_SMC |
2
|
-170.707
|
9.76e-32
|
-38.171
|
| Metro_vs_SMC |
3
|
-87.451
|
3.17e-26
|
-19.555
|
| Metro_vs_SMC |
4
|
-36.923
|
3.73e-19
|
-8.256
|
| DEMetro_Z_vs_SMC |
0
|
-29.188
|
3.02e-17
|
-6.527
|
| DEMetro_Z_vs_SMC |
1
|
-34.629
|
1.24e-18
|
-7.743
|
| DEMetro_Z_vs_SMC |
2
|
-44.056
|
1.35e-20
|
-9.851
|
| DEMetro_Z_vs_SMC |
3
|
-59.121
|
5.26e-23
|
-13.220
|
| DEMetro_Z_vs_SMC |
4
|
1.575
|
0.132
|
0.352
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
24.049 |
8.319 |
17.897 |
0.879 |
| HMC |
3.0 |
1.044 |
0.639 |
0.493 |
0.822 |
| HMC |
4.0 |
0.304 |
0.164 |
0.047 |
2.943 |
| HMC |
10.0 |
0.074 |
0.048 |
0.006 |
4.510 |
| HMC |
50.0 |
0.047 |
0.033 |
0.005 |
3.031 |
| SMC |
2.1 |
3041.344 |
8.319 |
17.897 |
169.471 |
| SMC |
3.0 |
414.083 |
0.639 |
0.493 |
838.185 |
| SMC |
4.0 |
184.440 |
0.164 |
0.047 |
3897.980 |
| SMC |
10.0 |
88.051 |
0.048 |
0.006 |
15438.243 |
| SMC |
50.0 |
6.432 |
0.033 |
0.005 |
1395.231 |
| Metro |
2.1 |
68.147 |
8.319 |
17.897 |
3.343 |
| Metro |
3.0 |
1.144 |
0.639 |
0.493 |
1.025 |
| Metro |
4.0 |
0.443 |
0.164 |
0.047 |
5.900 |
| Metro |
10.0 |
0.114 |
0.048 |
0.006 |
11.515 |
| Metro |
50.0 |
0.067 |
0.033 |
0.005 |
7.319 |
| DEMetro_Z |
2.1 |
825.584 |
8.319 |
17.897 |
45.665 |
| DEMetro_Z |
3.0 |
90.050 |
0.639 |
0.493 |
181.266 |
| DEMetro_Z |
4.0 |
37.861 |
0.164 |
0.047 |
797.399 |
| DEMetro_Z |
10.0 |
9.670 |
0.048 |
0.006 |
1687.856 |
| DEMetro_Z |
50.0 |
8.560 |
0.033 |
0.005 |
1859.398 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.812 |
0.0111 |
13.971 |
| HMC |
3.0 |
4.036 |
0.000702 |
21.890 |
| HMC |
4.0 |
3.839 |
0.00107 |
8.590 |
| HMC |
10.0 |
3.302 |
0.00241 |
1.428 |
| HMC |
50.0 |
0.301 |
0.765 |
0.084 |
| SMC |
2.1 |
325.240 |
3.35e-37 |
1509.402 |
| SMC |
3.0 |
240.106 |
1.45e-34 |
3248.487 |
| SMC |
4.0 |
303.155 |
1.7e-36 |
3500.432 |
| SMC |
10.0 |
152.825 |
7.85e-31 |
2903.634 |
| SMC |
50.0 |
54.552 |
2.35e-22 |
718.094 |
| Metro |
2.1 |
3.779 |
0.00127 |
75.782 |
| Metro |
3.0 |
6.215 |
5.56e-06 |
25.623 |
| Metro |
4.0 |
8.680 |
4.28e-08 |
21.265 |
| Metro |
10.0 |
15.236 |
1.21e-13 |
10.500 |
| Metro |
50.0 |
17.599 |
1.09e-17 |
7.683 |
| DEMetro_Z |
2.1 |
23.365 |
1.85e-15 |
724.848 |
| DEMetro_Z |
3.0 |
21.104 |
1.2e-14 |
1315.486 |
| DEMetro_Z |
4.0 |
21.283 |
1.02e-14 |
1309.606 |
| DEMetro_Z |
10.0 |
24.751 |
6.39e-16 |
733.131 |
| DEMetro_Z |
50.0 |
13.084 |
5.93e-11 |
697.978 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-16.957
|
6.25e-13
|
-3.792
|
| Metro_vs_DEMetro_Z |
1
|
-21.028
|
1.28e-14
|
-4.702
|
| Metro_vs_DEMetro_Z |
2
|
-20.763
|
1.61e-14
|
-4.643
|
| Metro_vs_DEMetro_Z |
3
|
-24.206
|
9.66e-16
|
-5.413
|
| Metro_vs_DEMetro_Z |
4
|
-12.955
|
7.04e-11
|
-2.897
|
| DEMetro_Z_vs_SMC |
0
|
-25.225
|
4.52e-16
|
-5.640
|
| DEMetro_Z_vs_SMC |
1
|
-29.856
|
1.98e-17
|
-6.676
|
| DEMetro_Z_vs_SMC |
2
|
-35.206
|
9.11e-19
|
-7.872
|
| DEMetro_Z_vs_SMC |
3
|
-53.489
|
3.48e-22
|
-11.960
|
| DEMetro_Z_vs_SMC |
4
|
-0.363
|
0.72
|
-0.081
|
| HMC_vs_DEMetro_Z |
0
|
-22.154
|
4.92e-15
|
-4.954
|
| HMC_vs_DEMetro_Z |
1
|
-20.608
|
1.85e-14
|
-4.608
|
| HMC_vs_DEMetro_Z |
2
|
-21.266
|
1.04e-14
|
-4.755
|
| HMC_vs_DEMetro_Z |
3
|
-24.721
|
6.55e-16
|
-5.528
|
| HMC_vs_DEMetro_Z |
4
|
-13.082
|
5.95e-11
|
-2.925
|
| HMC_vs_Metro |
0
|
-2.930
|
0.0086
|
-0.655
|
| HMC_vs_Metro |
1
|
-0.494
|
0.627
|
-0.111
|
| HMC_vs_Metro |
2
|
-3.489
|
0.00246
|
-0.780
|
| HMC_vs_Metro |
3
|
-10.955
|
1.19e-09
|
-2.450
|
| HMC_vs_Metro |
4
|
-17.254
|
4.58e-13
|
-3.858
|
| HMC_vs_SMC |
0
|
-279.953
|
8.12e-36
|
-62.599
|
| HMC_vs_SMC |
1
|
-206.822
|
2.55e-33
|
-46.247
|
| HMC_vs_SMC |
2
|
-275.556
|
1.1e-35
|
-61.616
|
| HMC_vs_SMC |
3
|
-153.056
|
7.76e-31
|
-34.224
|
| HMC_vs_SMC |
4
|
-54.486
|
2.46e-22
|
-12.183
|
| Metro_vs_SMC |
0
|
-67.620
|
4.14e-24
|
-15.120
|
| Metro_vs_SMC |
1
|
-236.867
|
1.94e-34
|
-52.965
|
| Metro_vs_SMC |
2
|
-292.874
|
3.45e-36
|
-65.489
|
| Metro_vs_SMC |
3
|
-154.995
|
6.11e-31
|
-34.658
|
| Metro_vs_SMC |
4
|
-54.083
|
2.83e-22
|
-12.093
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.508 |
0.116 |
0.028 |
13.971 |
| HMC |
3.0 |
0.165 |
0.064 |
0.005 |
21.890 |
| HMC |
4.0 |
0.073 |
0.049 |
0.003 |
8.590 |
| HMC |
10.0 |
0.037 |
0.033 |
0.002 |
1.428 |
| HMC |
50.0 |
0.029 |
0.029 |
0.002 |
0.084 |
| SMC |
2.1 |
42.456 |
0.116 |
0.028 |
1509.402 |
| SMC |
3.0 |
15.109 |
0.064 |
0.005 |
3248.487 |
| SMC |
4.0 |
9.873 |
0.049 |
0.003 |
3500.432 |
| SMC |
10.0 |
6.673 |
0.033 |
0.002 |
2903.634 |
| SMC |
50.0 |
1.372 |
0.029 |
0.002 |
718.094 |
| Metro |
2.1 |
2.242 |
0.116 |
0.028 |
75.782 |
| Metro |
3.0 |
0.183 |
0.064 |
0.005 |
25.623 |
| Metro |
4.0 |
0.109 |
0.049 |
0.003 |
21.265 |
| Metro |
10.0 |
0.057 |
0.033 |
0.002 |
10.500 |
| Metro |
50.0 |
0.044 |
0.029 |
0.002 |
7.683 |
| DEMetro_Z |
2.1 |
20.449 |
0.116 |
0.028 |
724.848 |
| DEMetro_Z |
3.0 |
6.157 |
0.064 |
0.005 |
1315.486 |
| DEMetro_Z |
4.0 |
3.724 |
0.049 |
0.003 |
1309.606 |
| DEMetro_Z |
10.0 |
1.710 |
0.033 |
0.002 |
733.131 |
| DEMetro_Z |
50.0 |
1.335 |
0.029 |
0.002 |
697.978 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.850 |
0.00108 |
33.541 |
| HMC |
3.0 |
3.544 |
0.00216 |
18.023 |
| HMC |
4.0 |
3.581 |
0.00191 |
6.386 |
| HMC |
10.0 |
2.264 |
0.0298 |
0.831 |
| HMC |
50.0 |
0.273 |
0.786 |
0.074 |
| SMC |
2.1 |
185.579 |
3.5e-34 |
233.263 |
| SMC |
3.0 |
201.688 |
4.8e-36 |
200.189 |
| SMC |
4.0 |
228.943 |
1.16e-35 |
320.057 |
| SMC |
10.0 |
158.971 |
2.87e-32 |
243.404 |
| SMC |
50.0 |
98.555 |
7.63e-28 |
183.843 |
| Metro |
2.1 |
8.292 |
9.76e-08 |
128.001 |
| Metro |
3.0 |
6.825 |
1.53e-06 |
20.701 |
| Metro |
4.0 |
10.131 |
3.3e-09 |
20.001 |
| Metro |
10.0 |
15.744 |
1.07e-14 |
9.000 |
| Metro |
50.0 |
15.366 |
2.77e-16 |
6.489 |
| DEMetro_Z |
2.1 |
67.117 |
3.73e-24 |
280.817 |
| DEMetro_Z |
3.0 |
64.571 |
7.19e-24 |
234.678 |
| DEMetro_Z |
4.0 |
63.357 |
1.24e-23 |
350.890 |
| DEMetro_Z |
10.0 |
54.478 |
2.02e-22 |
243.097 |
| DEMetro_Z |
50.0 |
31.604 |
6.5e-18 |
232.913 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
12.201
|
1.96e-10
|
2.728
|
| DEMetro_Z_vs_SMC |
1
|
8.899
|
3.33e-08
|
1.990
|
| DEMetro_Z_vs_SMC |
2
|
5.429
|
3.08e-05
|
1.214
|
| DEMetro_Z_vs_SMC |
3
|
-0.070
|
0.945
|
-0.016
|
| DEMetro_Z_vs_SMC |
4
|
6.838
|
1.59e-06
|
1.529
|
| HMC_vs_Metro |
0
|
-4.665
|
0.000169
|
-1.043
|
| HMC_vs_Metro |
1
|
-0.416
|
0.682
|
-0.093
|
| HMC_vs_Metro |
2
|
-4.942
|
9.05e-05
|
-1.105
|
| HMC_vs_Metro |
3
|
-11.469
|
5.54e-10
|
-2.565
|
| HMC_vs_Metro |
4
|
-15.708
|
2.44e-12
|
-3.512
|
| Metro_vs_DEMetro_Z |
0
|
-10.238
|
3.6e-09
|
-2.289
|
| Metro_vs_DEMetro_Z |
1
|
-46.011
|
5.96e-21
|
-10.288
|
| Metro_vs_DEMetro_Z |
2
|
-51.548
|
7e-22
|
-11.526
|
| Metro_vs_DEMetro_Z |
3
|
-50.106
|
1.2e-21
|
-11.204
|
| Metro_vs_DEMetro_Z |
4
|
-30.435
|
1.38e-17
|
-6.805
|
| HMC_vs_SMC |
0
|
-22.111
|
5.1e-15
|
-4.944
|
| HMC_vs_SMC |
1
|
-35.814
|
6.61e-19
|
-8.008
|
| HMC_vs_SMC |
2
|
-146.927
|
1.68e-30
|
-32.854
|
| HMC_vs_SMC |
3
|
-166.633
|
1.54e-31
|
-37.260
|
| HMC_vs_SMC |
4
|
-96.538
|
4.87e-27
|
-21.587
|
| Metro_vs_SMC |
0
|
-6.992
|
1.17e-06
|
-1.563
|
| Metro_vs_SMC |
1
|
-50.081
|
1.21e-21
|
-11.199
|
| Metro_vs_SMC |
2
|
-124.286
|
4.04e-29
|
-27.791
|
| Metro_vs_SMC |
3
|
-142.136
|
3.16e-30
|
-31.782
|
| Metro_vs_SMC |
4
|
-94.337
|
7.55e-27
|
-21.094
|
| HMC_vs_DEMetro_Z |
0
|
-22.560
|
3.53e-15
|
-5.045
|
| HMC_vs_DEMetro_Z |
1
|
-41.357
|
4.44e-20
|
-9.248
|
| HMC_vs_DEMetro_Z |
2
|
-60.866
|
3.03e-23
|
-13.610
|
| HMC_vs_DEMetro_Z |
3
|
-54.726
|
2.26e-22
|
-12.237
|
| HMC_vs_DEMetro_Z |
4
|
-31.619
|
6.79e-18
|
-7.070
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.071 |
0.015 |
0.002 |
33.541 |
| HMC |
3.0 |
0.050 |
0.015 |
0.002 |
18.023 |
| HMC |
4.0 |
0.023 |
0.015 |
0.001 |
6.386 |
| HMC |
10.0 |
0.015 |
0.014 |
0.002 |
0.831 |
| HMC |
50.0 |
0.014 |
0.014 |
0.002 |
0.074 |
| SMC |
2.1 |
0.407 |
0.015 |
0.002 |
233.263 |
| SMC |
3.0 |
0.406 |
0.015 |
0.002 |
200.189 |
| SMC |
4.0 |
0.402 |
0.015 |
0.001 |
320.057 |
| SMC |
10.0 |
0.398 |
0.014 |
0.002 |
243.404 |
| SMC |
50.0 |
0.306 |
0.014 |
0.002 |
183.843 |
| Metro |
2.1 |
0.230 |
0.015 |
0.002 |
128.001 |
| Metro |
3.0 |
0.055 |
0.015 |
0.002 |
20.701 |
| Metro |
4.0 |
0.039 |
0.015 |
0.001 |
20.001 |
| Metro |
10.0 |
0.028 |
0.014 |
0.002 |
9.000 |
| Metro |
50.0 |
0.024 |
0.014 |
0.002 |
6.489 |
| DEMetro_Z |
2.1 |
0.487 |
0.015 |
0.002 |
280.817 |
| DEMetro_Z |
3.0 |
0.474 |
0.015 |
0.002 |
234.678 |
| DEMetro_Z |
4.0 |
0.440 |
0.015 |
0.001 |
350.890 |
| DEMetro_Z |
10.0 |
0.398 |
0.014 |
0.002 |
243.097 |
| DEMetro_Z |
50.0 |
0.384 |
0.014 |
0.002 |
232.913 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.256 |
0.223 |
1.608 |
| HMC |
3.0 |
1.593 |
0.128 |
12.694 |
| HMC |
4.0 |
0.984 |
0.337 |
7.860 |
| HMC |
10.0 |
-2.783 |
0.00867 |
-0.767 |
| HMC |
50.0 |
-3.183 |
0.00292 |
-1.059 |
| SMC |
2.1 |
27.180 |
6.75e-17 |
61.285 |
| SMC |
3.0 |
23.788 |
1.2e-15 |
112.294 |
| SMC |
4.0 |
19.681 |
3.76e-14 |
79.628 |
| SMC |
10.0 |
22.719 |
1.52e-15 |
40.914 |
| SMC |
50.0 |
12.275 |
8.29e-11 |
16.049 |
| Metro |
2.1 |
5.018 |
6.9e-05 |
8.376 |
| Metro |
3.0 |
12.910 |
2.06e-11 |
13.368 |
| Metro |
4.0 |
13.545 |
1.96e-12 |
9.814 |
| Metro |
10.0 |
14.241 |
1.81e-14 |
6.948 |
| Metro |
50.0 |
12.041 |
1.48e-12 |
6.048 |
| DEMetro_Z |
2.1 |
20.287 |
2.44e-14 |
337.269 |
| DEMetro_Z |
3.0 |
17.084 |
5.46e-13 |
600.693 |
| DEMetro_Z |
4.0 |
16.245 |
1.34e-12 |
381.502 |
| DEMetro_Z |
10.0 |
19.854 |
3.6e-14 |
273.200 |
| DEMetro_Z |
50.0 |
12.648 |
1.05e-10 |
166.381 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-20.103
|
2.9e-14
|
-4.495
|
| HMC_vs_DEMetro_Z |
1
|
-15.057
|
5.15e-12
|
-3.367
|
| HMC_vs_DEMetro_Z |
2
|
-14.453
|
1.06e-11
|
-3.232
|
| HMC_vs_DEMetro_Z |
3
|
-19.951
|
3.33e-14
|
-4.461
|
| HMC_vs_DEMetro_Z |
4
|
-12.680
|
1.02e-10
|
-2.835
|
| Metro_vs_SMC |
0
|
-19.248
|
6.38e-14
|
-4.304
|
| Metro_vs_SMC |
1
|
-18.715
|
1.06e-13
|
-4.185
|
| Metro_vs_SMC |
2
|
-16.548
|
9.66e-13
|
-3.700
|
| Metro_vs_SMC |
3
|
-18.536
|
1.26e-13
|
-4.145
|
| Metro_vs_SMC |
4
|
-7.140
|
8.69e-07
|
-1.597
|
| Metro_vs_DEMetro_Z |
0
|
-19.870
|
3.58e-14
|
-4.443
|
| Metro_vs_DEMetro_Z |
1
|
-16.873
|
6.83e-13
|
-3.773
|
| Metro_vs_DEMetro_Z |
2
|
-15.741
|
2.35e-12
|
-3.520
|
| Metro_vs_DEMetro_Z |
3
|
-19.484
|
5.12e-14
|
-4.357
|
| Metro_vs_DEMetro_Z |
4
|
-12.095
|
2.27e-10
|
-2.704
|
| HMC_vs_Metro |
0
|
-3.139
|
0.00541
|
-0.702
|
| HMC_vs_Metro |
1
|
-0.081
|
0.936
|
-0.018
|
| HMC_vs_Metro |
2
|
-0.245
|
0.809
|
-0.055
|
| HMC_vs_Metro |
3
|
-16.945
|
6.33e-13
|
-3.789
|
| HMC_vs_Metro |
4
|
-14.892
|
6.25e-12
|
-3.330
|
| HMC_vs_SMC |
0
|
-22.275
|
4.45e-15
|
-4.981
|
| HMC_vs_SMC |
1
|
-12.285
|
1.74e-10
|
-2.747
|
| HMC_vs_SMC |
2
|
-8.946
|
3.07e-08
|
-2.000
|
| HMC_vs_SMC |
3
|
-23.107
|
2.27e-15
|
-5.167
|
| HMC_vs_SMC |
4
|
-13.276
|
4.61e-11
|
-2.969
|
| DEMetro_Z_vs_SMC |
0
|
16.533
|
9.82e-13
|
3.697
|
| DEMetro_Z_vs_SMC |
1
|
13.431
|
3.78e-11
|
3.003
|
| DEMetro_Z_vs_SMC |
2
|
12.248
|
1.83e-10
|
2.739
|
| DEMetro_Z_vs_SMC |
3
|
16.824
|
7.19e-13
|
3.762
|
| DEMetro_Z_vs_SMC |
4
|
11.200
|
8.24e-10
|
2.504
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.103 |
0.068 |
0.022 |
1.608 |
| HMC |
3.0 |
0.089 |
0.036 |
0.004 |
12.694 |
| HMC |
4.0 |
0.059 |
0.032 |
0.003 |
7.860 |
| HMC |
10.0 |
0.021 |
0.024 |
0.004 |
-0.767 |
| HMC |
50.0 |
0.019 |
0.022 |
0.003 |
-1.059 |
| SMC |
2.1 |
1.416 |
0.068 |
0.022 |
61.285 |
| SMC |
3.0 |
0.504 |
0.036 |
0.004 |
112.294 |
| SMC |
4.0 |
0.305 |
0.032 |
0.003 |
79.628 |
| SMC |
10.0 |
0.174 |
0.024 |
0.004 |
40.914 |
| SMC |
50.0 |
0.074 |
0.022 |
0.003 |
16.049 |
| Metro |
2.1 |
0.252 |
0.068 |
0.022 |
8.376 |
| Metro |
3.0 |
0.092 |
0.036 |
0.004 |
13.368 |
| Metro |
4.0 |
0.065 |
0.032 |
0.003 |
9.814 |
| Metro |
10.0 |
0.049 |
0.024 |
0.004 |
6.948 |
| Metro |
50.0 |
0.042 |
0.022 |
0.003 |
6.048 |
| DEMetro_Z |
2.1 |
7.485 |
0.068 |
0.022 |
337.269 |
| DEMetro_Z |
3.0 |
2.537 |
0.036 |
0.004 |
600.693 |
| DEMetro_Z |
4.0 |
1.342 |
0.032 |
0.003 |
381.502 |
| DEMetro_Z |
10.0 |
1.024 |
0.024 |
0.004 |
273.200 |
| DEMetro_Z |
50.0 |
0.560 |
0.022 |
0.003 |
166.381 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.036 |
0.972 |
-0.010 |
| HMC |
3.0 |
1.254 |
0.225 |
2.210 |
| HMC |
4.0 |
1.698 |
0.106 |
3.741 |
| HMC |
10.0 |
5.709 |
6.83e-06 |
3.664 |
| HMC |
50.0 |
7.632 |
3.65e-09 |
2.518 |
| SMC |
2.1 |
72.958 |
3.75e-25 |
157.484 |
| SMC |
3.0 |
84.473 |
5.82e-26 |
813.581 |
| SMC |
4.0 |
50.061 |
1.21e-21 |
3668.885 |
| SMC |
10.0 |
70.560 |
1.85e-24 |
13601.849 |
| SMC |
50.0 |
28.284 |
5.41e-17 |
1189.387 |
| Metro |
2.1 |
1.671 |
0.106 |
0.803 |
| Metro |
3.0 |
3.691 |
0.000879 |
1.663 |
| Metro |
4.0 |
3.863 |
0.000947 |
4.763 |
| Metro |
10.0 |
6.953 |
1.01e-06 |
10.995 |
| Metro |
50.0 |
11.939 |
4.42e-12 |
6.619 |
| DEMetro_Z |
2.1 |
7.967 |
1.59e-07 |
19.898 |
| DEMetro_Z |
3.0 |
10.151 |
4.07e-09 |
85.173 |
| DEMetro_Z |
4.0 |
8.200 |
1.16e-07 |
219.591 |
| DEMetro_Z |
10.0 |
5.870 |
1.18e-05 |
873.468 |
| DEMetro_Z |
50.0 |
3.852 |
0.00107 |
301.042 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-71.636
|
1.39e-24
|
-16.018
|
| HMC_vs_SMC |
1
|
-85.221
|
5.18e-26
|
-19.056
|
| HMC_vs_SMC |
2
|
-50.305
|
1.11e-21
|
-11.249
|
| HMC_vs_SMC |
3
|
-70.594
|
1.83e-24
|
-15.785
|
| HMC_vs_SMC |
4
|
-28.249
|
5.54e-17
|
-6.317
|
| Metro_vs_DEMetro_Z |
0
|
-7.393
|
5.3e-07
|
-1.653
|
| Metro_vs_DEMetro_Z |
1
|
-9.988
|
5.36e-09
|
-2.233
|
| Metro_vs_DEMetro_Z |
2
|
-8.073
|
1.46e-07
|
-1.805
|
| Metro_vs_DEMetro_Z |
3
|
-5.799
|
1.38e-05
|
-1.297
|
| Metro_vs_DEMetro_Z |
4
|
-3.775
|
0.00128
|
-0.844
|
| HMC_vs_Metro |
0
|
-2.022
|
0.0575
|
-0.452
|
| HMC_vs_Metro |
1
|
0.314
|
0.757
|
0.070
|
| HMC_vs_Metro |
2
|
-0.430
|
0.672
|
-0.096
|
| HMC_vs_Metro |
3
|
-3.865
|
0.00104
|
-0.864
|
| HMC_vs_Metro |
4
|
-6.325
|
4.54e-06
|
-1.414
|
| HMC_vs_DEMetro_Z |
0
|
-7.771
|
2.57e-07
|
-1.738
|
| HMC_vs_DEMetro_Z |
1
|
-9.247
|
1.83e-08
|
-2.068
|
| HMC_vs_DEMetro_Z |
2
|
-7.868
|
2.14e-07
|
-1.759
|
| HMC_vs_DEMetro_Z |
3
|
-5.844
|
1.25e-05
|
-1.307
|
| HMC_vs_DEMetro_Z |
4
|
-3.817
|
0.00116
|
-0.853
|
| Metro_vs_SMC |
0
|
-66.472
|
5.73e-24
|
-14.864
|
| Metro_vs_SMC |
1
|
-84.473
|
6.12e-26
|
-18.889
|
| Metro_vs_SMC |
2
|
-50.044
|
1.22e-21
|
-11.190
|
| Metro_vs_SMC |
3
|
-70.463
|
1.9e-24
|
-15.756
|
| Metro_vs_SMC |
4
|
-28.108
|
6.08e-17
|
-6.285
|
| DEMetro_Z_vs_SMC |
0
|
-42.753
|
2.38e-20
|
-9.560
|
| DEMetro_Z_vs_SMC |
1
|
-51.889
|
6.18e-22
|
-11.603
|
| DEMetro_Z_vs_SMC |
2
|
-45.575
|
7.14e-21
|
-10.191
|
| DEMetro_Z_vs_SMC |
3
|
-59.218
|
5.09e-23
|
-13.242
|
| DEMetro_Z_vs_SMC |
4
|
-9.815
|
7.1e-09
|
-2.195
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
8.140 |
8.319 |
17.897 |
-0.010 |
| HMC |
3.0 |
1.729 |
0.639 |
0.493 |
2.210 |
| HMC |
4.0 |
0.341 |
0.164 |
0.047 |
3.741 |
| HMC |
10.0 |
0.069 |
0.048 |
0.006 |
3.664 |
| HMC |
50.0 |
0.045 |
0.033 |
0.005 |
2.518 |
| SMC |
2.1 |
2826.811 |
8.319 |
17.897 |
157.484 |
| SMC |
3.0 |
401.947 |
0.639 |
0.493 |
813.581 |
| SMC |
4.0 |
173.609 |
0.164 |
0.047 |
3668.885 |
| SMC |
10.0 |
77.583 |
0.048 |
0.006 |
13601.849 |
| SMC |
50.0 |
5.488 |
0.033 |
0.005 |
1189.387 |
| Metro |
2.1 |
22.698 |
8.319 |
17.897 |
0.803 |
| Metro |
3.0 |
1.459 |
0.639 |
0.493 |
1.663 |
| Metro |
4.0 |
0.390 |
0.164 |
0.047 |
4.763 |
| Metro |
10.0 |
0.111 |
0.048 |
0.006 |
10.995 |
| Metro |
50.0 |
0.064 |
0.033 |
0.005 |
6.619 |
| DEMetro_Z |
2.1 |
364.430 |
8.319 |
17.897 |
19.898 |
| DEMetro_Z |
3.0 |
42.651 |
0.639 |
0.493 |
85.173 |
| DEMetro_Z |
4.0 |
10.545 |
0.164 |
0.047 |
219.591 |
| DEMetro_Z |
10.0 |
5.027 |
0.048 |
0.006 |
873.468 |
| DEMetro_Z |
50.0 |
1.414 |
0.033 |
0.005 |
301.042 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.067 |
0.00626 |
7.576 |
| HMC |
3.0 |
1.758 |
0.0949 |
39.977 |
| HMC |
4.0 |
1.453 |
0.163 |
18.535 |
| HMC |
10.0 |
2.364 |
0.0237 |
0.876 |
| HMC |
50.0 |
-0.415 |
0.68 |
-0.123 |
| SMC |
2.1 |
138.172 |
5.14e-30 |
1453.877 |
| SMC |
3.0 |
155.814 |
5.45e-31 |
3199.474 |
| SMC |
4.0 |
85.738 |
4.6e-26 |
3381.863 |
| SMC |
10.0 |
119.179 |
8.86e-29 |
2700.172 |
| SMC |
50.0 |
40.060 |
7.97e-20 |
644.463 |
| Metro |
2.1 |
3.792 |
0.00123 |
31.380 |
| Metro |
3.0 |
9.046 |
2.41e-08 |
31.609 |
| Metro |
4.0 |
7.327 |
5.58e-07 |
20.479 |
| Metro |
10.0 |
12.948 |
9.39e-12 |
10.750 |
| Metro |
50.0 |
14.956 |
1.86e-14 |
8.062 |
| DEMetro_Z |
2.1 |
17.027 |
5.79e-13 |
479.261 |
| DEMetro_Z |
3.0 |
18.216 |
1.73e-13 |
913.623 |
| DEMetro_Z |
4.0 |
13.495 |
3.48e-11 |
643.475 |
| DEMetro_Z |
10.0 |
14.927 |
5.99e-12 |
520.171 |
| DEMetro_Z |
50.0 |
11.751 |
3.68e-10 |
289.597 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-16.370
|
1.17e-12
|
-3.660
|
| Metro_vs_DEMetro_Z |
1
|
-17.967
|
2.21e-13
|
-4.018
|
| Metro_vs_DEMetro_Z |
2
|
-13.116
|
5.69e-11
|
-2.933
|
| Metro_vs_DEMetro_Z |
3
|
-14.708
|
7.77e-12
|
-3.289
|
| Metro_vs_DEMetro_Z |
4
|
-11.402
|
6.11e-10
|
-2.550
|
| DEMetro_Z_vs_SMC |
0
|
-32.273
|
4.63e-18
|
-7.217
|
| DEMetro_Z_vs_SMC |
1
|
-40.677
|
6.06e-20
|
-9.096
|
| DEMetro_Z_vs_SMC |
2
|
-48.622
|
2.11e-21
|
-10.872
|
| DEMetro_Z_vs_SMC |
3
|
-60.286
|
3.63e-23
|
-13.480
|
| DEMetro_Z_vs_SMC |
4
|
-11.230
|
7.87e-10
|
-2.511
|
| HMC_vs_DEMetro_Z |
0
|
-16.670
|
8.48e-13
|
-3.728
|
| HMC_vs_DEMetro_Z |
1
|
-13.845
|
2.23e-11
|
-3.096
|
| HMC_vs_DEMetro_Z |
2
|
-11.798
|
3.45e-10
|
-2.638
|
| HMC_vs_DEMetro_Z |
3
|
-14.916
|
6.08e-12
|
-3.335
|
| HMC_vs_DEMetro_Z |
4
|
-11.744
|
3.73e-10
|
-2.626
|
| HMC_vs_Metro |
0
|
-2.749
|
0.0128
|
-0.615
|
| HMC_vs_Metro |
1
|
0.371
|
0.715
|
0.083
|
| HMC_vs_Metro |
2
|
-0.149
|
0.883
|
-0.033
|
| HMC_vs_Metro |
3
|
-10.795
|
1.51e-09
|
-2.414
|
| HMC_vs_Metro |
4
|
-16.802
|
7.36e-13
|
-3.757
|
| HMC_vs_SMC |
0
|
-129.413
|
1.87e-29
|
-28.938
|
| HMC_vs_SMC |
1
|
-115.441
|
1.64e-28
|
-25.813
|
| HMC_vs_SMC |
2
|
-86.616
|
3.81e-26
|
-19.368
|
| HMC_vs_SMC |
3
|
-119.065
|
9.12e-29
|
-26.624
|
| HMC_vs_SMC |
4
|
-40.047
|
8.13e-20
|
-8.955
|
| Metro_vs_SMC |
0
|
-90.560
|
1.64e-26
|
-20.250
|
| Metro_vs_SMC |
1
|
-147.318
|
1.6e-30
|
-32.941
|
| Metro_vs_SMC |
2
|
-85.111
|
5.31e-26
|
-19.031
|
| Metro_vs_SMC |
3
|
-118.838
|
9.45e-29
|
-26.573
|
| Metro_vs_SMC |
4
|
-39.441
|
1.08e-19
|
-8.819
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.328 |
0.116 |
0.028 |
7.576 |
| HMC |
3.0 |
0.249 |
0.064 |
0.005 |
39.977 |
| HMC |
4.0 |
0.101 |
0.049 |
0.003 |
18.535 |
| HMC |
10.0 |
0.035 |
0.033 |
0.002 |
0.876 |
| HMC |
50.0 |
0.029 |
0.029 |
0.002 |
-0.123 |
| SMC |
2.1 |
40.898 |
0.116 |
0.028 |
1453.877 |
| SMC |
3.0 |
14.882 |
0.064 |
0.005 |
3199.474 |
| SMC |
4.0 |
9.540 |
0.049 |
0.003 |
3381.863 |
| SMC |
10.0 |
6.208 |
0.033 |
0.002 |
2700.172 |
| SMC |
50.0 |
1.235 |
0.029 |
0.002 |
644.463 |
| Metro |
2.1 |
0.996 |
0.116 |
0.028 |
31.380 |
| Metro |
3.0 |
0.210 |
0.064 |
0.005 |
31.609 |
| Metro |
4.0 |
0.107 |
0.049 |
0.003 |
20.479 |
| Metro |
10.0 |
0.058 |
0.033 |
0.002 |
10.750 |
| Metro |
50.0 |
0.044 |
0.029 |
0.002 |
8.062 |
| DEMetro_Z |
2.1 |
13.560 |
0.116 |
0.028 |
479.261 |
| DEMetro_Z |
3.0 |
4.295 |
0.064 |
0.005 |
913.623 |
| DEMetro_Z |
4.0 |
1.855 |
0.049 |
0.003 |
643.475 |
| DEMetro_Z |
10.0 |
1.223 |
0.033 |
0.002 |
520.171 |
| DEMetro_Z |
50.0 |
0.571 |
0.029 |
0.002 |
289.597 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.678 |
0.0149 |
33.221 |
| HMC |
3.0 |
1.783 |
0.0906 |
27.790 |
| HMC |
4.0 |
1.442 |
0.166 |
15.817 |
| HMC |
10.0 |
1.271 |
0.212 |
0.469 |
| HMC |
50.0 |
-0.940 |
0.353 |
-0.289 |
| SMC |
2.1 |
152.655 |
7.06e-32 |
238.162 |
| SMC |
3.0 |
184.168 |
1.1e-34 |
201.979 |
| SMC |
4.0 |
136.691 |
2.36e-30 |
320.705 |
| SMC |
10.0 |
159.102 |
2.91e-32 |
245.006 |
| SMC |
50.0 |
87.330 |
9.7e-27 |
174.595 |
| Metro |
2.1 |
6.423 |
3.69e-06 |
80.392 |
| Metro |
3.0 |
7.808 |
2.22e-07 |
23.325 |
| Metro |
4.0 |
9.093 |
1.98e-08 |
19.601 |
| Metro |
10.0 |
12.661 |
7.17e-12 |
9.044 |
| Metro |
50.0 |
13.444 |
6.63e-14 |
6.489 |
| DEMetro_Z |
2.1 |
58.624 |
5.38e-23 |
320.677 |
| DEMetro_Z |
3.0 |
46.289 |
4.71e-21 |
251.217 |
| DEMetro_Z |
4.0 |
29.758 |
2.06e-17 |
333.828 |
| DEMetro_Z |
10.0 |
34.299 |
1.4e-18 |
248.917 |
| DEMetro_Z |
50.0 |
17.681 |
2.89e-13 |
164.681 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
14.079
|
1.67e-11
|
3.148
|
| DEMetro_Z_vs_SMC |
1
|
8.961
|
2.99e-08
|
2.004
|
| DEMetro_Z_vs_SMC |
2
|
1.158
|
0.261
|
0.259
|
| DEMetro_Z_vs_SMC |
3
|
0.542
|
0.594
|
0.121
|
| DEMetro_Z_vs_SMC |
4
|
-1.001
|
0.329
|
-0.224
|
| HMC_vs_Metro |
0
|
-2.562
|
0.0191
|
-0.573
|
| HMC_vs_Metro |
1
|
0.285
|
0.779
|
0.064
|
| HMC_vs_Metro |
2
|
-0.337
|
0.74
|
-0.075
|
| HMC_vs_Metro |
3
|
-10.799
|
1.51e-09
|
-2.415
|
| HMC_vs_Metro |
4
|
-15.267
|
4.04e-12
|
-3.414
|
| Metro_vs_DEMetro_Z |
0
|
-17.016
|
5.88e-13
|
-3.805
|
| Metro_vs_DEMetro_Z |
1
|
-34.933
|
1.05e-18
|
-7.811
|
| Metro_vs_DEMetro_Z |
2
|
-27.468
|
9.32e-17
|
-6.142
|
| Metro_vs_DEMetro_Z |
3
|
-32.308
|
4.54e-18
|
-7.224
|
| Metro_vs_DEMetro_Z |
4
|
-16.755
|
7.74e-13
|
-3.747
|
| HMC_vs_SMC |
0
|
-16.026
|
1.71e-12
|
-3.584
|
| HMC_vs_SMC |
1
|
-11.055
|
1.02e-09
|
-2.472
|
| HMC_vs_SMC |
2
|
-26.982
|
1.3e-16
|
-6.033
|
| HMC_vs_SMC |
3
|
-156.930
|
4.83e-31
|
-35.091
|
| HMC_vs_SMC |
4
|
-88.398
|
2.59e-26
|
-19.766
|
| Metro_vs_SMC |
0
|
-12.532
|
1.24e-10
|
-2.802
|
| Metro_vs_SMC |
1
|
-62.100
|
2.07e-23
|
-13.886
|
| Metro_vs_SMC |
2
|
-105.181
|
9.58e-28
|
-23.519
|
| Metro_vs_SMC |
3
|
-126.339
|
2.96e-29
|
-28.250
|
| Metro_vs_SMC |
4
|
-83.341
|
7.91e-26
|
-18.636
|
| HMC_vs_DEMetro_Z |
0
|
-20.482
|
2.06e-14
|
-4.580
|
| HMC_vs_DEMetro_Z |
1
|
-12.010
|
2.55e-10
|
-2.686
|
| HMC_vs_DEMetro_Z |
2
|
-19.704
|
4.18e-14
|
-4.406
|
| HMC_vs_DEMetro_Z |
3
|
-34.914
|
1.06e-18
|
-7.807
|
| HMC_vs_DEMetro_Z |
4
|
-17.691
|
2.93e-13
|
-3.956
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.071 |
0.015 |
0.002 |
33.221 |
| HMC |
3.0 |
0.069 |
0.015 |
0.002 |
27.790 |
| HMC |
4.0 |
0.034 |
0.015 |
0.001 |
15.817 |
| HMC |
10.0 |
0.015 |
0.014 |
0.002 |
0.469 |
| HMC |
50.0 |
0.013 |
0.014 |
0.002 |
-0.289 |
| SMC |
2.1 |
0.416 |
0.015 |
0.002 |
238.162 |
| SMC |
3.0 |
0.410 |
0.015 |
0.002 |
201.979 |
| SMC |
4.0 |
0.403 |
0.015 |
0.001 |
320.705 |
| SMC |
10.0 |
0.401 |
0.014 |
0.002 |
245.006 |
| SMC |
50.0 |
0.292 |
0.014 |
0.002 |
174.595 |
| Metro |
2.1 |
0.150 |
0.015 |
0.002 |
80.392 |
| Metro |
3.0 |
0.060 |
0.015 |
0.002 |
23.325 |
| Metro |
4.0 |
0.039 |
0.015 |
0.001 |
19.601 |
| Metro |
10.0 |
0.028 |
0.014 |
0.002 |
9.044 |
| Metro |
50.0 |
0.024 |
0.014 |
0.002 |
6.489 |
| DEMetro_Z |
2.1 |
0.554 |
0.015 |
0.002 |
320.677 |
| DEMetro_Z |
3.0 |
0.506 |
0.015 |
0.002 |
251.217 |
| DEMetro_Z |
4.0 |
0.419 |
0.015 |
0.001 |
333.828 |
| DEMetro_Z |
10.0 |
0.407 |
0.014 |
0.002 |
248.917 |
| DEMetro_Z |
50.0 |
0.276 |
0.014 |
0.002 |
164.681 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Correlation
(MvStudentT,
nu,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.033 |
0.974 |
0.010 |
| HMC |
3.0 |
1.095 |
0.281 |
0.398 |
| HMC |
4.0 |
3.032 |
0.0045 |
1.104 |
| HMC |
10.0 |
0.337 |
0.738 |
0.109 |
| HMC |
50.0 |
1.377 |
0.178 |
0.607 |
| SMC |
2.1 |
2.055 |
0.0505 |
1.223 |
| SMC |
3.0 |
-0.356 |
0.724 |
-0.093 |
| SMC |
4.0 |
-0.015 |
0.988 |
-0.005 |
| SMC |
10.0 |
-0.867 |
0.392 |
-0.233 |
| SMC |
50.0 |
-1.029 |
0.311 |
-0.269 |
| Metro |
2.1 |
2.797 |
0.011 |
3.401 |
| Metro |
3.0 |
3.668 |
0.00151 |
4.783 |
| Metro |
4.0 |
6.087 |
5.5e-06 |
7.209 |
| Metro |
10.0 |
5.903 |
7.1e-06 |
5.640 |
| Metro |
50.0 |
4.016 |
0.00065 |
4.595 |
| DEMetro_Z |
2.1 |
2.683 |
0.0136 |
2.292 |
| DEMetro_Z |
3.0 |
3.146 |
0.0039 |
1.566 |
| DEMetro_Z |
4.0 |
3.696 |
0.00122 |
2.828 |
| DEMetro_Z |
10.0 |
3.450 |
0.00153 |
1.359 |
| DEMetro_Z |
50.0 |
3.305 |
0.00267 |
1.717 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.002
|
0.00732
|
-0.671
|
| HMC_vs_DEMetro_Z |
1
|
-2.172
|
0.0428
|
-0.486
|
| HMC_vs_DEMetro_Z |
2
|
-2.044
|
0.0551
|
-0.457
|
| HMC_vs_DEMetro_Z |
3
|
-3.431
|
0.0028
|
-0.767
|
| HMC_vs_DEMetro_Z |
4
|
-1.711
|
0.103
|
-0.383
|
| Metro_vs_SMC |
0
|
1.653
|
0.115
|
0.370
|
| Metro_vs_SMC |
1
|
3.920
|
0.00092
|
0.877
|
| Metro_vs_SMC |
2
|
6.199
|
5.9e-06
|
1.386
|
| Metro_vs_SMC |
3
|
6.019
|
8.62e-06
|
1.346
|
| Metro_vs_SMC |
4
|
4.152
|
0.000542
|
0.928
|
| Metro_vs_DEMetro_Z |
0
|
0.698
|
0.494
|
0.156
|
| Metro_vs_DEMetro_Z |
1
|
2.315
|
0.0319
|
0.518
|
| Metro_vs_DEMetro_Z |
2
|
2.724
|
0.0135
|
0.609
|
| Metro_vs_DEMetro_Z |
3
|
4.399
|
0.000308
|
0.984
|
| Metro_vs_DEMetro_Z |
4
|
2.301
|
0.0329
|
0.514
|
| HMC_vs_Metro |
0
|
-2.841
|
0.0104
|
-0.635
|
| HMC_vs_Metro |
1
|
-3.596
|
0.00193
|
-0.804
|
| HMC_vs_Metro |
2
|
-5.117
|
6.12e-05
|
-1.144
|
| HMC_vs_Metro |
3
|
-5.516
|
2.54e-05
|
-1.234
|
| HMC_vs_Metro |
4
|
-3.475
|
0.00253
|
-0.777
|
| HMC_vs_SMC |
0
|
-2.305
|
0.0326
|
-0.516
|
| HMC_vs_SMC |
1
|
1.976
|
0.0629
|
0.442
|
| HMC_vs_SMC |
2
|
3.868
|
0.00104
|
0.865
|
| HMC_vs_SMC |
3
|
1.385
|
0.182
|
0.310
|
| HMC_vs_SMC |
4
|
2.300
|
0.0329
|
0.514
|
| DEMetro_Z_vs_SMC |
0
|
2.064
|
0.053
|
0.461
|
| DEMetro_Z_vs_SMC |
1
|
3.435
|
0.00278
|
0.768
|
| DEMetro_Z_vs_SMC |
2
|
3.579
|
0.002
|
0.800
|
| DEMetro_Z_vs_SMC |
3
|
4.987
|
8.18e-05
|
1.115
|
| DEMetro_Z_vs_SMC |
4
|
3.992
|
0.00078
|
0.893
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.067 |
0.067 |
0.049 |
0.010 |
| HMC |
3.0 |
0.049 |
0.038 |
0.028 |
0.398 |
| HMC |
4.0 |
0.042 |
0.024 |
0.017 |
1.104 |
| HMC |
10.0 |
0.026 |
0.024 |
0.019 |
0.109 |
| HMC |
50.0 |
0.033 |
0.023 |
0.016 |
0.607 |
| SMC |
2.1 |
0.127 |
0.067 |
0.049 |
1.223 |
| SMC |
3.0 |
0.035 |
0.038 |
0.028 |
-0.093 |
| SMC |
4.0 |
0.024 |
0.024 |
0.017 |
-0.005 |
| SMC |
10.0 |
0.020 |
0.024 |
0.019 |
-0.233 |
| SMC |
50.0 |
0.019 |
0.023 |
0.016 |
-0.269 |
| Metro |
2.1 |
0.233 |
0.067 |
0.049 |
3.401 |
| Metro |
3.0 |
0.172 |
0.038 |
0.028 |
4.783 |
| Metro |
4.0 |
0.144 |
0.024 |
0.017 |
7.209 |
| Metro |
10.0 |
0.129 |
0.024 |
0.019 |
5.640 |
| Metro |
50.0 |
0.097 |
0.023 |
0.016 |
4.595 |
| DEMetro_Z |
2.1 |
0.179 |
0.067 |
0.049 |
2.292 |
| DEMetro_Z |
3.0 |
0.082 |
0.038 |
0.028 |
1.566 |
| DEMetro_Z |
4.0 |
0.071 |
0.024 |
0.017 |
2.828 |
| DEMetro_Z |
10.0 |
0.049 |
0.024 |
0.019 |
1.359 |
| DEMetro_Z |
50.0 |
0.051 |
0.023 |
0.016 |
1.717 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.954 |
0.35 |
-0.226 |
| HMC |
3.0 |
1.107 |
0.276 |
0.423 |
| HMC |
4.0 |
0.945 |
0.351 |
0.306 |
| HMC |
10.0 |
2.019 |
0.0557 |
1.599 |
| HMC |
50.0 |
1.566 |
0.127 |
0.658 |
| SMC |
2.1 |
2.708 |
0.0107 |
0.719 |
| SMC |
3.0 |
1.114 |
0.273 |
0.418 |
| SMC |
4.0 |
0.721 |
0.476 |
0.198 |
| SMC |
10.0 |
0.487 |
0.629 |
0.164 |
| SMC |
50.0 |
-0.142 |
0.888 |
-0.044 |
| Metro |
2.1 |
-0.369 |
0.715 |
-0.093 |
| Metro |
3.0 |
2.640 |
0.0139 |
1.481 |
| Metro |
4.0 |
2.166 |
0.0392 |
1.119 |
| Metro |
10.0 |
5.242 |
3.31e-05 |
5.039 |
| Metro |
50.0 |
4.043 |
0.000436 |
2.373 |
| DEMetro_Z |
2.1 |
-0.657 |
0.517 |
-0.157 |
| DEMetro_Z |
3.0 |
2.791 |
0.00901 |
1.254 |
| DEMetro_Z |
4.0 |
1.749 |
0.0947 |
1.646 |
| DEMetro_Z |
10.0 |
2.526 |
0.0174 |
1.234 |
| DEMetro_Z |
50.0 |
0.676 |
0.504 |
0.276 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-5.665
|
1.84e-05
|
-1.267
|
| HMC_vs_SMC |
1
|
0.013
|
0.99
|
0.003
|
| HMC_vs_SMC |
2
|
0.376
|
0.711
|
0.084
|
| HMC_vs_SMC |
3
|
1.714
|
0.103
|
0.383
|
| HMC_vs_SMC |
4
|
1.740
|
0.098
|
0.389
|
| Metro_vs_DEMetro_Z |
0
|
0.654
|
0.521
|
0.146
|
| Metro_vs_DEMetro_Z |
1
|
0.548
|
0.59
|
0.123
|
| Metro_vs_DEMetro_Z |
2
|
-0.519
|
0.61
|
-0.116
|
| Metro_vs_DEMetro_Z |
3
|
4.612
|
0.00019
|
1.031
|
| Metro_vs_DEMetro_Z |
4
|
3.359
|
0.0033
|
0.751
|
| HMC_vs_Metro |
0
|
-1.336
|
0.197
|
-0.299
|
| HMC_vs_Metro |
1
|
-1.827
|
0.0834
|
-0.409
|
| HMC_vs_Metro |
2
|
-1.599
|
0.126
|
-0.357
|
| HMC_vs_Metro |
3
|
-2.914
|
0.00889
|
-0.652
|
| HMC_vs_Metro |
4
|
-2.924
|
0.00872
|
-0.654
|
| HMC_vs_DEMetro_Z |
0
|
-2.320
|
0.0316
|
-0.519
|
| HMC_vs_DEMetro_Z |
1
|
-2.096
|
0.0497
|
-0.469
|
| HMC_vs_DEMetro_Z |
2
|
-1.317
|
0.204
|
-0.294
|
| HMC_vs_DEMetro_Z |
3
|
0.382
|
0.707
|
0.085
|
| HMC_vs_DEMetro_Z |
4
|
0.797
|
0.435
|
0.178
|
| Metro_vs_SMC |
0
|
-5.325
|
3.86e-05
|
-1.191
|
| Metro_vs_SMC |
1
|
2.079
|
0.0514
|
0.465
|
| Metro_vs_SMC |
2
|
1.779
|
0.0913
|
0.398
|
| Metro_vs_SMC |
3
|
4.839
|
0.000114
|
1.082
|
| Metro_vs_SMC |
4
|
4.222
|
0.000461
|
0.944
|
| DEMetro_Z_vs_SMC |
0
|
-5.009
|
7.78e-05
|
-1.120
|
| DEMetro_Z_vs_SMC |
1
|
1.909
|
0.0715
|
0.427
|
| DEMetro_Z_vs_SMC |
2
|
1.600
|
0.126
|
0.358
|
| DEMetro_Z_vs_SMC |
3
|
2.436
|
0.0249
|
0.545
|
| DEMetro_Z_vs_SMC |
4
|
0.720
|
0.48
|
0.161
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.023 |
8.853 |
16.927 |
-0.226 |
| HMC |
3.0 |
0.602 |
0.454 |
0.349 |
0.423 |
| HMC |
4.0 |
0.211 |
0.160 |
0.167 |
0.306 |
| HMC |
10.0 |
0.086 |
0.044 |
0.027 |
1.599 |
| HMC |
50.0 |
0.050 |
0.036 |
0.020 |
0.658 |
| SMC |
2.1 |
21.024 |
8.853 |
16.927 |
0.719 |
| SMC |
3.0 |
0.600 |
0.454 |
0.349 |
0.418 |
| SMC |
4.0 |
0.193 |
0.160 |
0.167 |
0.198 |
| SMC |
10.0 |
0.048 |
0.044 |
0.027 |
0.164 |
| SMC |
50.0 |
0.036 |
0.036 |
0.020 |
-0.044 |
| Metro |
2.1 |
7.273 |
8.853 |
16.927 |
-0.093 |
| Metro |
3.0 |
0.971 |
0.454 |
0.349 |
1.481 |
| Metro |
4.0 |
0.347 |
0.160 |
0.167 |
1.119 |
| Metro |
10.0 |
0.179 |
0.044 |
0.027 |
5.039 |
| Metro |
50.0 |
0.084 |
0.036 |
0.020 |
2.373 |
| DEMetro_Z |
2.1 |
6.200 |
8.853 |
16.927 |
-0.157 |
| DEMetro_Z |
3.0 |
0.892 |
0.454 |
0.349 |
1.254 |
| DEMetro_Z |
4.0 |
0.435 |
0.160 |
0.167 |
1.646 |
| DEMetro_Z |
10.0 |
0.077 |
0.044 |
0.027 |
1.234 |
| DEMetro_Z |
50.0 |
0.042 |
0.036 |
0.020 |
0.276 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.909 |
0.000377 |
1.162 |
| HMC |
3.0 |
4.236 |
0.000148 |
1.507 |
| HMC |
4.0 |
5.181 |
1.6e-05 |
2.510 |
| HMC |
10.0 |
2.018 |
0.0527 |
0.936 |
| HMC |
50.0 |
2.280 |
0.0303 |
1.109 |
| SMC |
2.1 |
11.109 |
7.68e-10 |
26.085 |
| SMC |
3.0 |
2.409 |
0.022 |
1.024 |
| SMC |
4.0 |
0.676 |
0.503 |
0.239 |
| SMC |
10.0 |
-0.931 |
0.358 |
-0.261 |
| SMC |
50.0 |
-0.578 |
0.568 |
-0.148 |
| Metro |
2.1 |
3.488 |
0.00237 |
6.270 |
| Metro |
3.0 |
6.421 |
2.79e-06 |
8.294 |
| Metro |
4.0 |
8.159 |
8.97e-08 |
12.104 |
| Metro |
10.0 |
7.290 |
4.21e-07 |
8.636 |
| Metro |
50.0 |
4.489 |
0.00023 |
7.080 |
| DEMetro_Z |
2.1 |
5.150 |
3.56e-05 |
4.112 |
| DEMetro_Z |
3.0 |
8.919 |
9.19e-10 |
4.306 |
| DEMetro_Z |
4.0 |
5.742 |
1.18e-05 |
6.767 |
| DEMetro_Z |
10.0 |
5.708 |
2.89e-06 |
2.513 |
| DEMetro_Z |
50.0 |
4.368 |
0.000193 |
2.637 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.097
|
0.287
|
0.245
|
| Metro_vs_DEMetro_Z |
1
|
3.132
|
0.00549
|
0.700
|
| Metro_vs_DEMetro_Z |
2
|
2.529
|
0.0204
|
0.566
|
| Metro_vs_DEMetro_Z |
3
|
5.093
|
6.47e-05
|
1.139
|
| Metro_vs_DEMetro_Z |
4
|
2.558
|
0.0192
|
0.572
|
| DEMetro_Z_vs_SMC |
0
|
-9.097
|
2.36e-08
|
-2.034
|
| DEMetro_Z_vs_SMC |
1
|
6.089
|
7.44e-06
|
1.362
|
| DEMetro_Z_vs_SMC |
2
|
5.689
|
1.75e-05
|
1.272
|
| DEMetro_Z_vs_SMC |
3
|
6.987
|
1.18e-06
|
1.562
|
| DEMetro_Z_vs_SMC |
4
|
5.077
|
6.7e-05
|
1.135
|
| HMC_vs_DEMetro_Z |
0
|
-3.609
|
0.00187
|
-0.807
|
| HMC_vs_DEMetro_Z |
1
|
-5.375
|
3.47e-05
|
-1.202
|
| HMC_vs_DEMetro_Z |
2
|
-3.334
|
0.00349
|
-0.745
|
| HMC_vs_DEMetro_Z |
3
|
-3.080
|
0.00616
|
-0.689
|
| HMC_vs_DEMetro_Z |
4
|
-1.905
|
0.072
|
-0.426
|
| HMC_vs_Metro |
0
|
-2.801
|
0.0114
|
-0.626
|
| HMC_vs_Metro |
1
|
-5.572
|
2.25e-05
|
-1.246
|
| HMC_vs_Metro |
2
|
-6.314
|
4.64e-06
|
-1.412
|
| HMC_vs_Metro |
3
|
-5.901
|
1.11e-05
|
-1.320
|
| HMC_vs_Metro |
4
|
-3.788
|
0.00124
|
-0.847
|
| HMC_vs_SMC |
0
|
-10.780
|
1.55e-09
|
-2.410
|
| HMC_vs_SMC |
1
|
1.148
|
0.265
|
0.257
|
| HMC_vs_SMC |
2
|
4.675
|
0.000165
|
1.045
|
| HMC_vs_SMC |
3
|
2.877
|
0.00966
|
0.643
|
| HMC_vs_SMC |
4
|
2.886
|
0.00947
|
0.645
|
| Metro_vs_SMC |
0
|
-8.769
|
4.18e-08
|
-1.961
|
| Metro_vs_SMC |
1
|
5.458
|
2.89e-05
|
1.220
|
| Metro_vs_SMC |
2
|
7.685
|
3.03e-07
|
1.718
|
| Metro_vs_SMC |
3
|
7.366
|
5.59e-07
|
1.647
|
| Metro_vs_SMC |
4
|
4.536
|
0.000226
|
1.014
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.165 |
0.119 |
0.040 |
1.162 |
| HMC |
3.0 |
0.092 |
0.063 |
0.019 |
1.507 |
| HMC |
4.0 |
0.068 |
0.045 |
0.009 |
2.510 |
| HMC |
10.0 |
0.046 |
0.035 |
0.012 |
0.936 |
| HMC |
50.0 |
0.042 |
0.031 |
0.010 |
1.109 |
| SMC |
2.1 |
1.154 |
0.119 |
0.040 |
26.085 |
| SMC |
3.0 |
0.083 |
0.063 |
0.019 |
1.024 |
| SMC |
4.0 |
0.047 |
0.045 |
0.009 |
0.239 |
| SMC |
10.0 |
0.032 |
0.035 |
0.012 |
-0.261 |
| SMC |
50.0 |
0.029 |
0.031 |
0.010 |
-0.148 |
| Metro |
2.1 |
0.368 |
0.119 |
0.040 |
6.270 |
| Metro |
3.0 |
0.223 |
0.063 |
0.019 |
8.294 |
| Metro |
4.0 |
0.157 |
0.045 |
0.009 |
12.104 |
| Metro |
10.0 |
0.135 |
0.035 |
0.012 |
8.636 |
| Metro |
50.0 |
0.102 |
0.031 |
0.010 |
7.080 |
| DEMetro_Z |
2.1 |
0.282 |
0.119 |
0.040 |
4.112 |
| DEMetro_Z |
3.0 |
0.146 |
0.063 |
0.019 |
4.306 |
| DEMetro_Z |
4.0 |
0.108 |
0.045 |
0.009 |
6.767 |
| DEMetro_Z |
10.0 |
0.064 |
0.035 |
0.012 |
2.513 |
| DEMetro_Z |
50.0 |
0.057 |
0.031 |
0.010 |
2.637 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.718 |
5.64e-05 |
2.261 |
| HMC |
3.0 |
3.191 |
0.00302 |
1.221 |
| HMC |
4.0 |
3.394 |
0.00198 |
1.569 |
| HMC |
10.0 |
3.017 |
0.00548 |
1.569 |
| HMC |
50.0 |
1.721 |
0.0948 |
0.717 |
| SMC |
2.1 |
16.296 |
9.2e-13 |
37.830 |
| SMC |
3.0 |
2.953 |
0.00623 |
1.432 |
| SMC |
4.0 |
-0.165 |
0.87 |
-0.059 |
| SMC |
10.0 |
-0.348 |
0.73 |
-0.130 |
| SMC |
50.0 |
-0.037 |
0.971 |
-0.010 |
| Metro |
2.1 |
6.158 |
5.08e-06 |
8.425 |
| Metro |
3.0 |
8.321 |
4.58e-08 |
8.591 |
| Metro |
4.0 |
8.718 |
1.6e-08 |
7.690 |
| Metro |
10.0 |
7.961 |
1.09e-07 |
9.444 |
| Metro |
50.0 |
4.424 |
0.000257 |
5.705 |
| DEMetro_Z |
2.1 |
5.370 |
2.71e-05 |
6.101 |
| DEMetro_Z |
3.0 |
7.467 |
8.43e-08 |
4.529 |
| DEMetro_Z |
4.0 |
5.083 |
4.02e-05 |
3.878 |
| DEMetro_Z |
10.0 |
5.148 |
2.48e-05 |
3.037 |
| DEMetro_Z |
50.0 |
3.532 |
0.00159 |
2.030 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-14.684
|
8e-12
|
-3.283
|
| DEMetro_Z_vs_SMC |
1
|
4.550
|
0.000219
|
1.017
|
| DEMetro_Z_vs_SMC |
2
|
5.140
|
5.82e-05
|
1.149
|
| DEMetro_Z_vs_SMC |
3
|
5.452
|
2.93e-05
|
1.219
|
| DEMetro_Z_vs_SMC |
4
|
4.208
|
0.000477
|
0.941
|
| HMC_vs_Metro |
0
|
-4.291
|
0.000395
|
-0.959
|
| HMC_vs_Metro |
1
|
-7.680
|
3.06e-07
|
-1.717
|
| HMC_vs_Metro |
2
|
-6.807
|
1.69e-06
|
-1.522
|
| HMC_vs_Metro |
3
|
-6.151
|
6.53e-06
|
-1.375
|
| HMC_vs_Metro |
4
|
-3.830
|
0.00113
|
-0.856
|
| Metro_vs_DEMetro_Z |
0
|
1.380
|
0.184
|
0.309
|
| Metro_vs_DEMetro_Z |
1
|
3.747
|
0.00137
|
0.838
|
| Metro_vs_DEMetro_Z |
2
|
3.201
|
0.0047
|
0.716
|
| Metro_vs_DEMetro_Z |
3
|
4.533
|
0.000228
|
1.014
|
| Metro_vs_DEMetro_Z |
4
|
2.533
|
0.0203
|
0.566
|
| HMC_vs_SMC |
0
|
-16.092
|
1.59e-12
|
-3.598
|
| HMC_vs_SMC |
1
|
-0.417
|
0.682
|
-0.093
|
| HMC_vs_SMC |
2
|
3.415
|
0.0029
|
0.764
|
| HMC_vs_SMC |
3
|
3.072
|
0.00628
|
0.687
|
| HMC_vs_SMC |
4
|
2.046
|
0.0549
|
0.457
|
| Metro_vs_SMC |
0
|
-12.754
|
9.2e-11
|
-2.852
|
| Metro_vs_SMC |
1
|
5.906
|
1.1e-05
|
1.321
|
| Metro_vs_SMC |
2
|
8.961
|
2.99e-08
|
2.004
|
| Metro_vs_SMC |
3
|
7.501
|
4.3e-07
|
1.677
|
| Metro_vs_SMC |
4
|
4.440
|
0.000281
|
0.993
|
| HMC_vs_DEMetro_Z |
0
|
-3.301
|
0.00376
|
-0.738
|
| HMC_vs_DEMetro_Z |
1
|
-4.515
|
0.000237
|
-1.010
|
| HMC_vs_DEMetro_Z |
2
|
-3.529
|
0.00224
|
-0.789
|
| HMC_vs_DEMetro_Z |
3
|
-2.160
|
0.0437
|
-0.483
|
| HMC_vs_DEMetro_Z |
4
|
-1.867
|
0.0774
|
-0.417
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.026 |
0.014 |
0.005 |
2.261 |
| HMC |
3.0 |
0.021 |
0.015 |
0.005 |
1.221 |
| HMC |
4.0 |
0.022 |
0.014 |
0.005 |
1.569 |
| HMC |
10.0 |
0.022 |
0.015 |
0.005 |
1.569 |
| HMC |
50.0 |
0.020 |
0.015 |
0.006 |
0.717 |
| SMC |
2.1 |
0.209 |
0.014 |
0.005 |
37.830 |
| SMC |
3.0 |
0.022 |
0.015 |
0.005 |
1.432 |
| SMC |
4.0 |
0.014 |
0.014 |
0.005 |
-0.059 |
| SMC |
10.0 |
0.014 |
0.015 |
0.005 |
-0.130 |
| SMC |
50.0 |
0.015 |
0.015 |
0.006 |
-0.010 |
| Metro |
2.1 |
0.058 |
0.014 |
0.005 |
8.425 |
| Metro |
3.0 |
0.059 |
0.015 |
0.005 |
8.591 |
| Metro |
4.0 |
0.050 |
0.014 |
0.005 |
7.690 |
| Metro |
10.0 |
0.060 |
0.015 |
0.005 |
9.444 |
| Metro |
50.0 |
0.049 |
0.015 |
0.006 |
5.705 |
| DEMetro_Z |
2.1 |
0.046 |
0.014 |
0.005 |
6.101 |
| DEMetro_Z |
3.0 |
0.038 |
0.015 |
0.005 |
4.529 |
| DEMetro_Z |
4.0 |
0.032 |
0.014 |
0.005 |
3.878 |
| DEMetro_Z |
10.0 |
0.029 |
0.015 |
0.005 |
3.037 |
| DEMetro_Z |
50.0 |
0.027 |
0.015 |
0.006 |
2.030 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.158 |
0.255 |
0.433 |
| HMC |
3.0 |
1.217 |
0.232 |
0.468 |
| HMC |
4.0 |
2.342 |
0.0269 |
1.242 |
| HMC |
10.0 |
1.049 |
0.301 |
0.326 |
| HMC |
50.0 |
1.772 |
0.0857 |
0.725 |
| SMC |
2.1 |
3.150 |
0.00369 |
1.441 |
| SMC |
3.0 |
-0.334 |
0.741 |
-0.088 |
| SMC |
4.0 |
0.325 |
0.747 |
0.098 |
| SMC |
10.0 |
-0.675 |
0.504 |
-0.190 |
| SMC |
50.0 |
-1.632 |
0.113 |
-0.427 |
| Metro |
2.1 |
1.892 |
0.0737 |
7.513 |
| Metro |
3.0 |
2.996 |
0.00731 |
6.672 |
| Metro |
4.0 |
5.612 |
1.59e-05 |
6.633 |
| Metro |
10.0 |
4.170 |
0.000448 |
4.648 |
| Metro |
50.0 |
3.864 |
0.000885 |
3.686 |
| DEMetro_Z |
2.1 |
1.121 |
0.273 |
0.624 |
| DEMetro_Z |
3.0 |
2.324 |
0.0284 |
1.335 |
| DEMetro_Z |
4.0 |
3.732 |
0.000939 |
2.090 |
| DEMetro_Z |
10.0 |
2.412 |
0.0214 |
0.943 |
| DEMetro_Z |
50.0 |
2.428 |
0.0213 |
1.098 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.340
|
0.737
|
-0.076
|
| HMC_vs_DEMetro_Z |
1
|
-1.321
|
0.202
|
-0.295
|
| HMC_vs_DEMetro_Z |
2
|
-1.333
|
0.198
|
-0.298
|
| HMC_vs_DEMetro_Z |
3
|
-1.600
|
0.126
|
-0.358
|
| HMC_vs_DEMetro_Z |
4
|
-0.726
|
0.477
|
-0.162
|
| Metro_vs_SMC |
0
|
1.477
|
0.156
|
0.330
|
| Metro_vs_SMC |
1
|
3.063
|
0.0064
|
0.685
|
| Metro_vs_SMC |
2
|
5.878
|
1.16e-05
|
1.314
|
| Metro_vs_SMC |
3
|
4.445
|
0.000278
|
0.994
|
| Metro_vs_SMC |
4
|
4.313
|
0.000375
|
0.964
|
| Metro_vs_DEMetro_Z |
0
|
1.698
|
0.106
|
0.380
|
| Metro_vs_DEMetro_Z |
1
|
2.401
|
0.0268
|
0.537
|
| Metro_vs_DEMetro_Z |
2
|
4.269
|
0.000415
|
0.955
|
| Metro_vs_DEMetro_Z |
3
|
3.389
|
0.00308
|
0.758
|
| Metro_vs_DEMetro_Z |
4
|
2.698
|
0.0142
|
0.603
|
| HMC_vs_Metro |
0
|
-1.776
|
0.0918
|
-0.397
|
| HMC_vs_Metro |
1
|
-2.758
|
0.0125
|
-0.617
|
| HMC_vs_Metro |
2
|
-3.981
|
0.000799
|
-0.890
|
| HMC_vs_Metro |
3
|
-3.846
|
0.00109
|
-0.860
|
| HMC_vs_Metro |
4
|
-2.795
|
0.0115
|
-0.625
|
| HMC_vs_SMC |
0
|
-2.567
|
0.0189
|
-0.574
|
| HMC_vs_SMC |
1
|
1.787
|
0.09
|
0.399
|
| HMC_vs_SMC |
2
|
2.114
|
0.048
|
0.473
|
| HMC_vs_SMC |
3
|
1.826
|
0.0836
|
0.408
|
| HMC_vs_SMC |
4
|
3.127
|
0.00555
|
0.699
|
| DEMetro_Z_vs_SMC |
0
|
-1.539
|
0.14
|
-0.344
|
| DEMetro_Z_vs_SMC |
1
|
2.602
|
0.0175
|
0.582
|
| DEMetro_Z_vs_SMC |
2
|
4.082
|
0.000635
|
0.913
|
| DEMetro_Z_vs_SMC |
3
|
2.983
|
0.00764
|
0.667
|
| DEMetro_Z_vs_SMC |
4
|
4.212
|
0.000473
|
0.942
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.088 |
0.067 |
0.049 |
0.433 |
| HMC |
3.0 |
0.051 |
0.038 |
0.028 |
0.468 |
| HMC |
4.0 |
0.045 |
0.024 |
0.017 |
1.242 |
| HMC |
10.0 |
0.030 |
0.024 |
0.019 |
0.326 |
| HMC |
50.0 |
0.035 |
0.023 |
0.016 |
0.725 |
| SMC |
2.1 |
0.137 |
0.067 |
0.049 |
1.441 |
| SMC |
3.0 |
0.036 |
0.038 |
0.028 |
-0.088 |
| SMC |
4.0 |
0.026 |
0.024 |
0.017 |
0.098 |
| SMC |
10.0 |
0.021 |
0.024 |
0.019 |
-0.190 |
| SMC |
50.0 |
0.016 |
0.023 |
0.016 |
-0.427 |
| Metro |
2.1 |
0.433 |
0.067 |
0.049 |
7.513 |
| Metro |
3.0 |
0.225 |
0.038 |
0.028 |
6.672 |
| Metro |
4.0 |
0.135 |
0.024 |
0.017 |
6.633 |
| Metro |
10.0 |
0.110 |
0.024 |
0.019 |
4.648 |
| Metro |
50.0 |
0.083 |
0.023 |
0.016 |
3.686 |
| DEMetro_Z |
2.1 |
0.097 |
0.067 |
0.049 |
0.624 |
| DEMetro_Z |
3.0 |
0.075 |
0.038 |
0.028 |
1.335 |
| DEMetro_Z |
4.0 |
0.059 |
0.024 |
0.017 |
2.090 |
| DEMetro_Z |
10.0 |
0.042 |
0.024 |
0.019 |
0.943 |
| DEMetro_Z |
50.0 |
0.041 |
0.023 |
0.016 |
1.098 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.891 |
0.382 |
-0.211 |
| HMC |
3.0 |
1.537 |
0.134 |
0.644 |
| HMC |
4.0 |
1.995 |
0.0551 |
0.895 |
| HMC |
10.0 |
2.009 |
0.0543 |
1.006 |
| HMC |
50.0 |
0.208 |
0.836 |
0.071 |
| SMC |
2.1 |
0.216 |
0.831 |
0.053 |
| SMC |
3.0 |
0.866 |
0.393 |
0.351 |
| SMC |
4.0 |
0.893 |
0.378 |
0.239 |
| SMC |
10.0 |
-1.370 |
0.179 |
-0.391 |
| SMC |
50.0 |
-1.135 |
0.264 |
-0.322 |
| Metro |
2.1 |
0.686 |
0.5 |
0.534 |
| Metro |
3.0 |
1.541 |
0.139 |
3.671 |
| Metro |
4.0 |
3.367 |
0.00181 |
1.201 |
| Metro |
10.0 |
5.012 |
4.71e-05 |
3.752 |
| Metro |
50.0 |
4.238 |
0.000298 |
2.877 |
| DEMetro_Z |
2.1 |
-0.667 |
0.511 |
-0.159 |
| DEMetro_Z |
3.0 |
2.574 |
0.0172 |
1.978 |
| DEMetro_Z |
4.0 |
3.106 |
0.00358 |
1.003 |
| DEMetro_Z |
10.0 |
1.777 |
0.0849 |
0.732 |
| DEMetro_Z |
50.0 |
2.055 |
0.0493 |
1.011 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-2.237
|
0.0375
|
-0.500
|
| HMC_vs_SMC |
1
|
1.077
|
0.295
|
0.241
|
| HMC_vs_SMC |
2
|
1.575
|
0.132
|
0.352
|
| HMC_vs_SMC |
3
|
3.201
|
0.00471
|
0.716
|
| HMC_vs_SMC |
4
|
1.137
|
0.27
|
0.254
|
| Metro_vs_DEMetro_Z |
0
|
0.914
|
0.372
|
0.204
|
| Metro_vs_DEMetro_Z |
1
|
0.689
|
0.499
|
0.154
|
| Metro_vs_DEMetro_Z |
2
|
0.600
|
0.555
|
0.134
|
| Metro_vs_DEMetro_Z |
3
|
5.467
|
2.83e-05
|
1.222
|
| Metro_vs_DEMetro_Z |
4
|
2.219
|
0.0388
|
0.496
|
| HMC_vs_Metro |
0
|
-0.985
|
0.337
|
-0.220
|
| HMC_vs_Metro |
1
|
-1.273
|
0.218
|
-0.285
|
| HMC_vs_Metro |
2
|
-0.671
|
0.51
|
-0.150
|
| HMC_vs_Metro |
3
|
-3.408
|
0.00295
|
-0.762
|
| HMC_vs_Metro |
4
|
-4.644
|
0.000177
|
-1.038
|
| HMC_vs_DEMetro_Z |
0
|
-0.891
|
0.384
|
-0.199
|
| HMC_vs_DEMetro_Z |
1
|
-1.726
|
0.101
|
-0.386
|
| HMC_vs_DEMetro_Z |
2
|
-0.232
|
0.819
|
-0.052
|
| HMC_vs_DEMetro_Z |
3
|
0.524
|
0.607
|
0.117
|
| HMC_vs_DEMetro_Z |
4
|
-1.764
|
0.0937
|
-0.395
|
| Metro_vs_SMC |
0
|
0.618
|
0.544
|
0.138
|
| Metro_vs_SMC |
1
|
1.393
|
0.18
|
0.312
|
| Metro_vs_SMC |
2
|
3.618
|
0.00183
|
0.809
|
| Metro_vs_SMC |
3
|
5.622
|
2.02e-05
|
1.257
|
| Metro_vs_SMC |
4
|
4.554
|
0.000217
|
1.018
|
| DEMetro_Z_vs_SMC |
0
|
-2.143
|
0.0453
|
-0.479
|
| DEMetro_Z_vs_SMC |
1
|
2.496
|
0.0219
|
0.558
|
| DEMetro_Z_vs_SMC |
2
|
3.597
|
0.00192
|
0.804
|
| DEMetro_Z_vs_SMC |
3
|
3.054
|
0.00652
|
0.683
|
| DEMetro_Z_vs_SMC |
4
|
2.955
|
0.00813
|
0.661
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.274 |
8.853 |
16.927 |
-0.211 |
| HMC |
3.0 |
0.679 |
0.454 |
0.349 |
0.644 |
| HMC |
4.0 |
0.309 |
0.160 |
0.167 |
0.895 |
| HMC |
10.0 |
0.071 |
0.044 |
0.027 |
1.006 |
| HMC |
50.0 |
0.038 |
0.036 |
0.020 |
0.071 |
| SMC |
2.1 |
9.743 |
8.853 |
16.927 |
0.053 |
| SMC |
3.0 |
0.577 |
0.454 |
0.349 |
0.351 |
| SMC |
4.0 |
0.200 |
0.160 |
0.167 |
0.239 |
| SMC |
10.0 |
0.033 |
0.044 |
0.027 |
-0.391 |
| SMC |
50.0 |
0.030 |
0.036 |
0.020 |
-0.322 |
| Metro |
2.1 |
17.888 |
8.853 |
16.927 |
0.534 |
| Metro |
3.0 |
1.737 |
0.454 |
0.349 |
3.671 |
| Metro |
4.0 |
0.360 |
0.160 |
0.167 |
1.201 |
| Metro |
10.0 |
0.144 |
0.044 |
0.027 |
3.752 |
| Metro |
50.0 |
0.094 |
0.036 |
0.020 |
2.877 |
| DEMetro_Z |
2.1 |
6.157 |
8.853 |
16.927 |
-0.159 |
| DEMetro_Z |
3.0 |
1.145 |
0.454 |
0.349 |
1.978 |
| DEMetro_Z |
4.0 |
0.327 |
0.160 |
0.167 |
1.003 |
| DEMetro_Z |
10.0 |
0.063 |
0.044 |
0.027 |
0.732 |
| DEMetro_Z |
50.0 |
0.057 |
0.036 |
0.020 |
1.011 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.484 |
0.0187 |
1.096 |
| HMC |
3.0 |
3.916 |
0.00051 |
1.893 |
| HMC |
4.0 |
4.783 |
8.42e-05 |
3.655 |
| HMC |
10.0 |
2.107 |
0.0418 |
0.705 |
| HMC |
50.0 |
2.097 |
0.0447 |
0.979 |
| SMC |
2.1 |
6.573 |
2.4e-06 |
13.084 |
| SMC |
3.0 |
1.049 |
0.301 |
0.340 |
| SMC |
4.0 |
1.869 |
0.0693 |
0.588 |
| SMC |
10.0 |
-1.486 |
0.147 |
-0.400 |
| SMC |
50.0 |
-2.006 |
0.0545 |
-0.503 |
| Metro |
2.1 |
2.364 |
0.0288 |
9.799 |
| Metro |
3.0 |
3.701 |
0.00149 |
9.959 |
| Metro |
4.0 |
7.151 |
6.86e-07 |
11.795 |
| Metro |
10.0 |
5.670 |
1.49e-05 |
7.654 |
| Metro |
50.0 |
5.541 |
1.76e-05 |
5.870 |
| DEMetro_Z |
2.1 |
5.835 |
2.79e-06 |
2.882 |
| DEMetro_Z |
3.0 |
4.610 |
0.000143 |
4.109 |
| DEMetro_Z |
4.0 |
8.558 |
1e-08 |
5.672 |
| DEMetro_Z |
10.0 |
5.315 |
6.13e-06 |
1.991 |
| DEMetro_Z |
50.0 |
4.879 |
3.25e-05 |
2.208 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.614
|
0.123
|
0.361
|
| Metro_vs_DEMetro_Z |
1
|
2.141
|
0.0454
|
0.479
|
| Metro_vs_DEMetro_Z |
2
|
3.938
|
0.000882
|
0.881
|
| Metro_vs_DEMetro_Z |
3
|
4.364
|
0.000334
|
0.976
|
| Metro_vs_DEMetro_Z |
4
|
3.324
|
0.00356
|
0.743
|
| DEMetro_Z_vs_SMC |
0
|
-5.355
|
3.62e-05
|
-1.197
|
| DEMetro_Z_vs_SMC |
1
|
4.414
|
0.000298
|
0.987
|
| DEMetro_Z_vs_SMC |
2
|
7.961
|
1.8e-07
|
1.780
|
| DEMetro_Z_vs_SMC |
3
|
7.981
|
1.74e-07
|
1.785
|
| DEMetro_Z_vs_SMC |
4
|
7.442
|
4.82e-07
|
1.664
|
| HMC_vs_DEMetro_Z |
0
|
-3.183
|
0.0049
|
-0.712
|
| HMC_vs_DEMetro_Z |
1
|
-2.330
|
0.031
|
-0.521
|
| HMC_vs_DEMetro_Z |
2
|
-2.572
|
0.0187
|
-0.575
|
| HMC_vs_DEMetro_Z |
3
|
-3.390
|
0.00307
|
-0.758
|
| HMC_vs_DEMetro_Z |
4
|
-2.116
|
0.0477
|
-0.473
|
| HMC_vs_Metro |
0
|
-2.057
|
0.0537
|
-0.460
|
| HMC_vs_Metro |
1
|
-2.932
|
0.00855
|
-0.656
|
| HMC_vs_Metro |
2
|
-4.650
|
0.000174
|
-1.040
|
| HMC_vs_Metro |
3
|
-4.944
|
9.01e-05
|
-1.106
|
| HMC_vs_Metro |
4
|
-4.162
|
0.00053
|
-0.931
|
| HMC_vs_SMC |
0
|
-5.775
|
1.45e-05
|
-1.291
|
| HMC_vs_SMC |
1
|
3.554
|
0.00212
|
0.795
|
| HMC_vs_SMC |
2
|
3.930
|
0.000899
|
0.879
|
| HMC_vs_SMC |
3
|
3.879
|
0.00101
|
0.867
|
| HMC_vs_SMC |
4
|
3.636
|
0.00176
|
0.813
|
| Metro_vs_SMC |
0
|
-0.628
|
0.538
|
-0.140
|
| Metro_vs_SMC |
1
|
3.537
|
0.0022
|
0.791
|
| Metro_vs_SMC |
2
|
6.853
|
1.54e-06
|
1.532
|
| Metro_vs_SMC |
3
|
6.187
|
6.05e-06
|
1.383
|
| Metro_vs_SMC |
4
|
6.047
|
8.13e-06
|
1.352
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.162 |
0.119 |
0.040 |
1.096 |
| HMC |
3.0 |
0.100 |
0.063 |
0.019 |
1.893 |
| HMC |
4.0 |
0.079 |
0.045 |
0.009 |
3.655 |
| HMC |
10.0 |
0.043 |
0.035 |
0.012 |
0.705 |
| HMC |
50.0 |
0.041 |
0.031 |
0.010 |
0.979 |
| SMC |
2.1 |
0.638 |
0.119 |
0.040 |
13.084 |
| SMC |
3.0 |
0.070 |
0.063 |
0.019 |
0.340 |
| SMC |
4.0 |
0.050 |
0.045 |
0.009 |
0.588 |
| SMC |
10.0 |
0.030 |
0.035 |
0.012 |
-0.400 |
| SMC |
50.0 |
0.026 |
0.031 |
0.010 |
-0.503 |
| Metro |
2.1 |
0.508 |
0.119 |
0.040 |
9.799 |
| Metro |
3.0 |
0.255 |
0.063 |
0.019 |
9.959 |
| Metro |
4.0 |
0.154 |
0.045 |
0.009 |
11.795 |
| Metro |
10.0 |
0.124 |
0.035 |
0.012 |
7.654 |
| Metro |
50.0 |
0.090 |
0.031 |
0.010 |
5.870 |
| DEMetro_Z |
2.1 |
0.233 |
0.119 |
0.040 |
2.882 |
| DEMetro_Z |
3.0 |
0.142 |
0.063 |
0.019 |
4.109 |
| DEMetro_Z |
4.0 |
0.097 |
0.045 |
0.009 |
5.672 |
| DEMetro_Z |
10.0 |
0.058 |
0.035 |
0.012 |
1.991 |
| DEMetro_Z |
50.0 |
0.053 |
0.031 |
0.010 |
2.208 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.559 |
0.00146 |
1.987 |
| HMC |
3.0 |
3.109 |
0.00436 |
1.611 |
| HMC |
4.0 |
4.719 |
6.64e-05 |
2.520 |
| HMC |
10.0 |
2.127 |
0.0406 |
0.810 |
| HMC |
50.0 |
1.743 |
0.0913 |
0.757 |
| SMC |
2.1 |
8.413 |
7.24e-08 |
25.550 |
| SMC |
3.0 |
1.333 |
0.191 |
0.481 |
| SMC |
4.0 |
0.415 |
0.68 |
0.125 |
| SMC |
10.0 |
-1.700 |
0.0974 |
-0.514 |
| SMC |
50.0 |
-1.696 |
0.102 |
-0.411 |
| Metro |
2.1 |
5.652 |
1.64e-05 |
9.103 |
| Metro |
3.0 |
7.974 |
1.12e-07 |
9.907 |
| Metro |
4.0 |
7.954 |
7.64e-08 |
7.137 |
| Metro |
10.0 |
6.182 |
4.97e-06 |
9.052 |
| Metro |
50.0 |
5.292 |
3.07e-05 |
5.448 |
| DEMetro_Z |
2.1 |
5.337 |
1.95e-05 |
3.724 |
| DEMetro_Z |
3.0 |
5.119 |
2.87e-05 |
3.165 |
| DEMetro_Z |
4.0 |
6.948 |
2.54e-07 |
4.038 |
| DEMetro_Z |
10.0 |
5.081 |
2.25e-05 |
2.550 |
| DEMetro_Z |
50.0 |
5.060 |
1.71e-05 |
2.149 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-7.194
|
7.82e-07
|
-1.609
|
| DEMetro_Z_vs_SMC |
1
|
4.086
|
0.00063
|
0.914
|
| DEMetro_Z_vs_SMC |
2
|
6.548
|
2.86e-06
|
1.464
|
| DEMetro_Z_vs_SMC |
3
|
7.174
|
8.12e-07
|
1.604
|
| DEMetro_Z_vs_SMC |
4
|
7.156
|
8.43e-07
|
1.600
|
| HMC_vs_Metro |
0
|
-4.273
|
0.000411
|
-0.955
|
| HMC_vs_Metro |
1
|
-6.120
|
6.97e-06
|
-1.368
|
| HMC_vs_Metro |
2
|
-4.248
|
0.000435
|
-0.950
|
| HMC_vs_Metro |
3
|
-5.425
|
3.1e-05
|
-1.213
|
| HMC_vs_Metro |
4
|
-4.145
|
0.000551
|
-0.927
|
| Metro_vs_DEMetro_Z |
0
|
2.998
|
0.0074
|
0.670
|
| Metro_vs_DEMetro_Z |
1
|
4.816
|
0.00012
|
1.077
|
| Metro_vs_DEMetro_Z |
2
|
2.879
|
0.00962
|
0.644
|
| Metro_vs_DEMetro_Z |
3
|
4.697
|
0.000157
|
1.050
|
| Metro_vs_DEMetro_Z |
4
|
2.894
|
0.0093
|
0.647
|
| HMC_vs_SMC |
0
|
-7.634
|
3.34e-07
|
-1.707
|
| HMC_vs_SMC |
1
|
2.379
|
0.028
|
0.532
|
| HMC_vs_SMC |
2
|
4.689
|
0.00016
|
1.049
|
| HMC_vs_SMC |
3
|
3.692
|
0.00155
|
0.825
|
| HMC_vs_SMC |
4
|
3.400
|
0.003
|
0.760
|
| Metro_vs_SMC |
0
|
-4.943
|
9.02e-05
|
-1.105
|
| Metro_vs_SMC |
1
|
7.817
|
2.36e-07
|
1.748
|
| Metro_vs_SMC |
2
|
8.274
|
1.01e-07
|
1.850
|
| Metro_vs_SMC |
3
|
6.878
|
1.46e-06
|
1.538
|
| Metro_vs_SMC |
4
|
5.705
|
1.69e-05
|
1.276
|
| HMC_vs_DEMetro_Z |
0
|
-2.118
|
0.0476
|
-0.474
|
| HMC_vs_DEMetro_Z |
1
|
-2.507
|
0.0214
|
-0.561
|
| HMC_vs_DEMetro_Z |
2
|
-2.191
|
0.0412
|
-0.490
|
| HMC_vs_DEMetro_Z |
3
|
-3.149
|
0.00528
|
-0.704
|
| HMC_vs_DEMetro_Z |
4
|
-2.724
|
0.0135
|
-0.609
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.025 |
0.014 |
0.005 |
1.987 |
| HMC |
3.0 |
0.023 |
0.015 |
0.005 |
1.611 |
| HMC |
4.0 |
0.026 |
0.014 |
0.005 |
2.520 |
| HMC |
10.0 |
0.019 |
0.015 |
0.005 |
0.810 |
| HMC |
50.0 |
0.020 |
0.015 |
0.006 |
0.757 |
| SMC |
2.1 |
0.146 |
0.014 |
0.005 |
25.550 |
| SMC |
3.0 |
0.017 |
0.015 |
0.005 |
0.481 |
| SMC |
4.0 |
0.015 |
0.014 |
0.005 |
0.125 |
| SMC |
10.0 |
0.012 |
0.015 |
0.005 |
-0.514 |
| SMC |
50.0 |
0.013 |
0.015 |
0.006 |
-0.411 |
| Metro |
2.1 |
0.061 |
0.014 |
0.005 |
9.103 |
| Metro |
3.0 |
0.066 |
0.015 |
0.005 |
9.907 |
| Metro |
4.0 |
0.047 |
0.014 |
0.005 |
7.137 |
| Metro |
10.0 |
0.058 |
0.015 |
0.005 |
9.052 |
| Metro |
50.0 |
0.048 |
0.015 |
0.006 |
5.448 |
| DEMetro_Z |
2.1 |
0.033 |
0.014 |
0.005 |
3.724 |
| DEMetro_Z |
3.0 |
0.031 |
0.015 |
0.005 |
3.165 |
| DEMetro_Z |
4.0 |
0.033 |
0.014 |
0.005 |
4.038 |
| DEMetro_Z |
10.0 |
0.027 |
0.015 |
0.005 |
2.550 |
| DEMetro_Z |
50.0 |
0.028 |
0.015 |
0.006 |
2.149 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Tails_with_high_Multimodality
(Mixture,
nu,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.985 |
7.95e-06 |
9.853 |
| HMC |
3.0 |
6.143 |
5.95e-06 |
12.306 |
| HMC |
4.0 |
6.484 |
3.01e-06 |
15.987 |
| HMC |
10.0 |
4.286 |
0.000395 |
20.197 |
| HMC |
50.0 |
5.025 |
7.49e-05 |
40.253 |
| SMC |
2.1 |
5.172 |
4.66e-05 |
7.319 |
| SMC |
3.0 |
2.655 |
0.0143 |
2.061 |
| SMC |
4.0 |
1.063 |
0.295 |
0.300 |
| SMC |
10.0 |
-0.956 |
0.345 |
-0.279 |
| SMC |
50.0 |
0.307 |
0.761 |
0.116 |
| Metro |
2.1 |
6.432 |
1.21e-06 |
4.215 |
| Metro |
3.0 |
6.046 |
7.33e-06 |
12.189 |
| Metro |
4.0 |
4.516 |
0.000232 |
15.365 |
| Metro |
10.0 |
4.988 |
8.09e-05 |
27.645 |
| Metro |
50.0 |
5.166 |
5.46e-05 |
35.569 |
| DEMetro_Z |
2.1 |
4.909 |
9.48e-05 |
15.453 |
| DEMetro_Z |
3.0 |
4.870 |
0.000103 |
13.936 |
| DEMetro_Z |
4.0 |
5.053 |
6.89e-05 |
17.585 |
| DEMetro_Z |
10.0 |
8.635 |
4.84e-08 |
25.828 |
| DEMetro_Z |
50.0 |
4.777 |
0.00013 |
29.390 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.885
|
0.0748
|
-0.422
|
| HMC_vs_DEMetro_Z |
1
|
-0.420
|
0.679
|
-0.094
|
| HMC_vs_DEMetro_Z |
2
|
-0.348
|
0.732
|
-0.078
|
| HMC_vs_DEMetro_Z |
3
|
-1.008
|
0.326
|
-0.225
|
| HMC_vs_DEMetro_Z |
4
|
1.355
|
0.191
|
0.303
|
| Metro_vs_SMC |
0
|
-2.054
|
0.054
|
-0.459
|
| Metro_vs_SMC |
1
|
4.756
|
0.000137
|
1.064
|
| Metro_vs_SMC |
2
|
4.374
|
0.000326
|
0.978
|
| Metro_vs_SMC |
3
|
4.995
|
8.04e-05
|
1.117
|
| Metro_vs_SMC |
4
|
5.106
|
6.27e-05
|
1.142
|
| Metro_vs_DEMetro_Z |
0
|
-3.810
|
0.00118
|
-0.852
|
| Metro_vs_DEMetro_Z |
1
|
-0.606
|
0.552
|
-0.135
|
| Metro_vs_DEMetro_Z |
2
|
-0.426
|
0.675
|
-0.095
|
| Metro_vs_DEMetro_Z |
3
|
0.291
|
0.774
|
0.065
|
| Metro_vs_DEMetro_Z |
4
|
0.817
|
0.424
|
0.183
|
| HMC_vs_Metro |
0
|
3.653
|
0.00169
|
0.817
|
| HMC_vs_Metro |
1
|
0.035
|
0.972
|
0.008
|
| HMC_vs_Metro |
2
|
0.140
|
0.89
|
0.031
|
| HMC_vs_Metro |
3
|
-1.558
|
0.136
|
-0.348
|
| HMC_vs_Metro |
4
|
0.775
|
0.448
|
0.173
|
| HMC_vs_SMC |
0
|
1.090
|
0.289
|
0.244
|
| HMC_vs_SMC |
1
|
4.430
|
0.000288
|
0.991
|
| HMC_vs_SMC |
2
|
6.435
|
3.61e-06
|
1.439
|
| HMC_vs_SMC |
3
|
4.308
|
0.000379
|
0.963
|
| HMC_vs_SMC |
4
|
4.970
|
8.49e-05
|
1.111
|
| DEMetro_Z_vs_SMC |
0
|
2.625
|
0.0167
|
0.587
|
| DEMetro_Z_vs_SMC |
1
|
3.996
|
0.000774
|
0.893
|
| DEMetro_Z_vs_SMC |
2
|
5.011
|
7.77e-05
|
1.120
|
| DEMetro_Z_vs_SMC |
3
|
8.794
|
3.99e-08
|
1.966
|
| DEMetro_Z_vs_SMC |
4
|
4.706
|
0.000154
|
1.052
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.752 |
0.086 |
0.068 |
9.853 |
| HMC |
3.0 |
1.178 |
0.125 |
0.086 |
12.306 |
| HMC |
4.0 |
1.590 |
0.110 |
0.093 |
15.987 |
| HMC |
10.0 |
1.733 |
0.126 |
0.080 |
20.197 |
| HMC |
50.0 |
2.423 |
0.089 |
0.058 |
40.253 |
| SMC |
2.1 |
0.581 |
0.086 |
0.068 |
7.319 |
| SMC |
3.0 |
0.301 |
0.125 |
0.086 |
2.061 |
| SMC |
4.0 |
0.138 |
0.110 |
0.093 |
0.300 |
| SMC |
10.0 |
0.104 |
0.126 |
0.080 |
-0.279 |
| SMC |
50.0 |
0.096 |
0.089 |
0.058 |
0.116 |
| Metro |
2.1 |
0.371 |
0.086 |
0.068 |
4.215 |
| Metro |
3.0 |
1.168 |
0.125 |
0.086 |
12.189 |
| Metro |
4.0 |
1.533 |
0.110 |
0.093 |
15.365 |
| Metro |
10.0 |
2.325 |
0.126 |
0.080 |
27.645 |
| Metro |
50.0 |
2.152 |
0.089 |
0.058 |
35.569 |
| DEMetro_Z |
2.1 |
1.131 |
0.086 |
0.068 |
15.453 |
| DEMetro_Z |
3.0 |
1.318 |
0.125 |
0.086 |
13.936 |
| DEMetro_Z |
4.0 |
1.738 |
0.110 |
0.093 |
17.585 |
| DEMetro_Z |
10.0 |
2.181 |
0.126 |
0.080 |
25.828 |
| DEMetro_Z |
50.0 |
1.793 |
0.089 |
0.058 |
29.390 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.242 |
0.228 |
-0.283 |
| HMC |
3.0 |
3.694 |
0.00149 |
7.483 |
| HMC |
4.0 |
4.374 |
0.000324 |
22.837 |
| HMC |
10.0 |
3.357 |
0.00331 |
37.614 |
| HMC |
50.0 |
3.730 |
0.00142 |
78.671 |
| SMC |
2.1 |
-1.496 |
0.151 |
-0.335 |
| SMC |
3.0 |
2.309 |
0.0292 |
1.302 |
| SMC |
4.0 |
0.313 |
0.756 |
0.108 |
| SMC |
10.0 |
0.761 |
0.452 |
0.227 |
| SMC |
50.0 |
-0.325 |
0.747 |
-0.092 |
| Metro |
2.1 |
-1.571 |
0.133 |
-0.352 |
| Metro |
3.0 |
3.631 |
0.00175 |
10.857 |
| Metro |
4.0 |
2.861 |
0.01 |
27.602 |
| Metro |
10.0 |
3.489 |
0.00245 |
60.443 |
| Metro |
50.0 |
3.706 |
0.0015 |
59.948 |
| DEMetro_Z |
2.1 |
-1.181 |
0.251 |
-0.268 |
| DEMetro_Z |
3.0 |
3.590 |
0.00193 |
11.664 |
| DEMetro_Z |
4.0 |
3.372 |
0.0032 |
31.440 |
| DEMetro_Z |
10.0 |
5.731 |
1.58e-05 |
38.781 |
| DEMetro_Z |
50.0 |
2.618 |
0.0169 |
44.092 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.023
|
0.319
|
0.229
|
| HMC_vs_SMC |
1
|
2.850
|
0.0102
|
0.637
|
| HMC_vs_SMC |
2
|
4.353
|
0.000343
|
0.973
|
| HMC_vs_SMC |
3
|
3.372
|
0.0032
|
0.754
|
| HMC_vs_SMC |
4
|
3.740
|
0.00139
|
0.836
|
| Metro_vs_DEMetro_Z |
0
|
-2.486
|
0.0224
|
-0.556
|
| Metro_vs_DEMetro_Z |
1
|
-0.213
|
0.833
|
-0.048
|
| Metro_vs_DEMetro_Z |
2
|
-0.256
|
0.801
|
-0.057
|
| Metro_vs_DEMetro_Z |
3
|
1.182
|
0.252
|
0.264
|
| Metro_vs_DEMetro_Z |
4
|
0.717
|
0.482
|
0.160
|
| HMC_vs_Metro |
0
|
1.568
|
0.133
|
0.351
|
| HMC_vs_Metro |
1
|
-0.843
|
0.41
|
-0.189
|
| HMC_vs_Metro |
2
|
-0.422
|
0.678
|
-0.094
|
| HMC_vs_Metro |
3
|
-1.585
|
0.13
|
-0.354
|
| HMC_vs_Metro |
4
|
0.948
|
0.355
|
0.212
|
| HMC_vs_DEMetro_Z |
0
|
-0.292
|
0.773
|
-0.065
|
| HMC_vs_DEMetro_Z |
1
|
-0.981
|
0.339
|
-0.219
|
| HMC_vs_DEMetro_Z |
2
|
-0.737
|
0.47
|
-0.165
|
| HMC_vs_DEMetro_Z |
3
|
-0.085
|
0.934
|
-0.019
|
| HMC_vs_DEMetro_Z |
4
|
1.552
|
0.137
|
0.347
|
| Metro_vs_SMC |
0
|
-0.795
|
0.437
|
-0.178
|
| Metro_vs_SMC |
1
|
3.124
|
0.00558
|
0.699
|
| Metro_vs_SMC |
2
|
2.830
|
0.0107
|
0.633
|
| Metro_vs_SMC |
3
|
3.484
|
0.00248
|
0.779
|
| Metro_vs_SMC |
4
|
3.707
|
0.0015
|
0.829
|
| DEMetro_Z_vs_SMC |
0
|
1.698
|
0.106
|
0.380
|
| DEMetro_Z_vs_SMC |
1
|
3.127
|
0.00555
|
0.699
|
| DEMetro_Z_vs_SMC |
2
|
3.408
|
0.00295
|
0.762
|
| DEMetro_Z_vs_SMC |
3
|
5.697
|
1.72e-05
|
1.274
|
| DEMetro_Z_vs_SMC |
4
|
2.620
|
0.0169
|
0.586
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.424 |
17.896 |
40.526 |
-0.283 |
| HMC |
3.0 |
3.069 |
0.600 |
0.330 |
7.483 |
| HMC |
4.0 |
5.075 |
0.356 |
0.207 |
22.837 |
| HMC |
10.0 |
8.022 |
0.202 |
0.208 |
37.614 |
| HMC |
50.0 |
14.167 |
0.210 |
0.177 |
78.671 |
| SMC |
2.1 |
4.324 |
17.896 |
40.526 |
-0.335 |
| SMC |
3.0 |
1.029 |
0.600 |
0.330 |
1.302 |
| SMC |
4.0 |
0.378 |
0.356 |
0.207 |
0.108 |
| SMC |
10.0 |
0.250 |
0.202 |
0.208 |
0.227 |
| SMC |
50.0 |
0.193 |
0.210 |
0.177 |
-0.092 |
| Metro |
2.1 |
3.629 |
17.896 |
40.526 |
-0.352 |
| Metro |
3.0 |
4.182 |
0.600 |
0.330 |
10.857 |
| Metro |
4.0 |
6.060 |
0.356 |
0.207 |
27.602 |
| Metro |
10.0 |
12.768 |
0.202 |
0.208 |
60.443 |
| Metro |
50.0 |
10.846 |
0.210 |
0.177 |
59.948 |
| DEMetro_Z |
2.1 |
7.052 |
17.896 |
40.526 |
-0.268 |
| DEMetro_Z |
3.0 |
4.448 |
0.600 |
0.330 |
11.664 |
| DEMetro_Z |
4.0 |
6.853 |
0.356 |
0.207 |
31.440 |
| DEMetro_Z |
10.0 |
8.265 |
0.202 |
0.208 |
38.781 |
| DEMetro_Z |
50.0 |
8.033 |
0.210 |
0.177 |
44.092 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.976 |
7.21e-06 |
7.415 |
| HMC |
3.0 |
6.359 |
3.73e-06 |
12.369 |
| HMC |
4.0 |
6.375 |
3.83e-06 |
17.329 |
| HMC |
10.0 |
4.391 |
0.000312 |
22.928 |
| HMC |
50.0 |
5.020 |
7.57e-05 |
44.227 |
| SMC |
2.1 |
7.123 |
4.84e-07 |
6.890 |
| SMC |
3.0 |
3.125 |
0.00478 |
2.299 |
| SMC |
4.0 |
0.847 |
0.403 |
0.239 |
| SMC |
10.0 |
-1.013 |
0.318 |
-0.300 |
| SMC |
50.0 |
0.649 |
0.521 |
0.250 |
| Metro |
2.1 |
6.356 |
6.12e-07 |
3.034 |
| Metro |
3.0 |
6.423 |
3.26e-06 |
12.439 |
| Metro |
4.0 |
4.545 |
0.000218 |
16.179 |
| Metro |
10.0 |
4.761 |
0.000135 |
31.601 |
| Metro |
50.0 |
5.229 |
4.75e-05 |
38.803 |
| DEMetro_Z |
2.1 |
4.932 |
8.78e-05 |
11.275 |
| DEMetro_Z |
3.0 |
5.098 |
6.15e-05 |
14.254 |
| DEMetro_Z |
4.0 |
5.096 |
6.28e-05 |
19.089 |
| DEMetro_Z |
10.0 |
8.318 |
8.83e-08 |
29.997 |
| DEMetro_Z |
50.0 |
4.638 |
0.000179 |
31.959 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.789
|
0.00124
|
-0.847
|
| Metro_vs_DEMetro_Z |
1
|
-0.624
|
0.54
|
-0.139
|
| Metro_vs_DEMetro_Z |
2
|
-0.532
|
0.601
|
-0.119
|
| Metro_vs_DEMetro_Z |
3
|
0.218
|
0.83
|
0.049
|
| Metro_vs_DEMetro_Z |
4
|
0.812
|
0.427
|
0.181
|
| DEMetro_Z_vs_SMC |
0
|
1.886
|
0.0746
|
0.422
|
| DEMetro_Z_vs_SMC |
1
|
4.113
|
0.000592
|
0.920
|
| DEMetro_Z_vs_SMC |
2
|
5.079
|
6.66e-05
|
1.136
|
| DEMetro_Z_vs_SMC |
3
|
8.464
|
7.19e-08
|
1.893
|
| DEMetro_Z_vs_SMC |
4
|
4.553
|
0.000217
|
1.018
|
| HMC_vs_DEMetro_Z |
0
|
-1.788
|
0.0897
|
-0.400
|
| HMC_vs_DEMetro_Z |
1
|
-0.493
|
0.628
|
-0.110
|
| HMC_vs_DEMetro_Z |
2
|
-0.351
|
0.729
|
-0.079
|
| HMC_vs_DEMetro_Z |
3
|
-1.170
|
0.256
|
-0.262
|
| HMC_vs_DEMetro_Z |
4
|
1.374
|
0.185
|
0.307
|
| HMC_vs_Metro |
0
|
3.856
|
0.00106
|
0.862
|
| HMC_vs_Metro |
1
|
-0.022
|
0.982
|
-0.005
|
| HMC_vs_Metro |
2
|
0.244
|
0.81
|
0.055
|
| HMC_vs_Metro |
3
|
-1.536
|
0.141
|
-0.343
|
| HMC_vs_Metro |
4
|
0.787
|
0.441
|
0.176
|
| HMC_vs_SMC |
0
|
0.326
|
0.748
|
0.073
|
| HMC_vs_SMC |
1
|
4.581
|
0.000204
|
1.024
|
| HMC_vs_SMC |
2
|
6.350
|
4.3e-06
|
1.420
|
| HMC_vs_SMC |
3
|
4.424
|
0.000292
|
0.989
|
| HMC_vs_SMC |
4
|
4.949
|
8.91e-05
|
1.107
|
| Metro_vs_SMC |
0
|
-3.714
|
0.00147
|
-0.831
|
| Metro_vs_SMC |
1
|
4.983
|
8.26e-05
|
1.114
|
| Metro_vs_SMC |
2
|
4.419
|
0.000295
|
0.988
|
| Metro_vs_SMC |
3
|
4.766
|
0.000134
|
1.066
|
| Metro_vs_SMC |
4
|
5.145
|
5.75e-05
|
1.150
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.803 |
0.180 |
0.084 |
7.415 |
| HMC |
3.0 |
1.083 |
0.153 |
0.075 |
12.369 |
| HMC |
4.0 |
1.484 |
0.136 |
0.078 |
17.329 |
| HMC |
10.0 |
1.544 |
0.132 |
0.062 |
22.928 |
| HMC |
50.0 |
2.216 |
0.101 |
0.048 |
44.227 |
| SMC |
2.1 |
0.759 |
0.180 |
0.084 |
6.890 |
| SMC |
3.0 |
0.326 |
0.153 |
0.075 |
2.299 |
| SMC |
4.0 |
0.155 |
0.136 |
0.078 |
0.239 |
| SMC |
10.0 |
0.114 |
0.132 |
0.062 |
-0.300 |
| SMC |
50.0 |
0.113 |
0.101 |
0.048 |
0.250 |
| Metro |
2.1 |
0.435 |
0.180 |
0.084 |
3.034 |
| Metro |
3.0 |
1.088 |
0.153 |
0.075 |
12.439 |
| Metro |
4.0 |
1.394 |
0.136 |
0.078 |
16.179 |
| Metro |
10.0 |
2.078 |
0.132 |
0.062 |
31.601 |
| Metro |
50.0 |
1.957 |
0.101 |
0.048 |
38.803 |
| DEMetro_Z |
2.1 |
1.128 |
0.180 |
0.084 |
11.275 |
| DEMetro_Z |
3.0 |
1.225 |
0.153 |
0.075 |
14.254 |
| DEMetro_Z |
4.0 |
1.620 |
0.136 |
0.078 |
19.089 |
| DEMetro_Z |
10.0 |
1.979 |
0.132 |
0.062 |
29.997 |
| DEMetro_Z |
50.0 |
1.630 |
0.101 |
0.048 |
31.959 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.594 |
1.96e-05 |
11.037 |
| HMC |
3.0 |
5.812 |
1.26e-05 |
14.419 |
| HMC |
4.0 |
6.366 |
3.92e-06 |
17.764 |
| HMC |
10.0 |
4.376 |
0.000323 |
23.427 |
| HMC |
50.0 |
5.120 |
6.05e-05 |
39.589 |
| SMC |
2.1 |
5.889 |
9.49e-06 |
8.757 |
| SMC |
3.0 |
2.720 |
0.0125 |
2.266 |
| SMC |
4.0 |
0.857 |
0.397 |
0.241 |
| SMC |
10.0 |
-0.834 |
0.41 |
-0.238 |
| SMC |
50.0 |
0.255 |
0.8 |
0.090 |
| Metro |
2.1 |
6.319 |
2.04e-06 |
4.752 |
| Metro |
3.0 |
5.690 |
1.64e-05 |
14.080 |
| Metro |
4.0 |
4.493 |
0.000245 |
17.260 |
| Metro |
10.0 |
5.172 |
5.38e-05 |
31.428 |
| Metro |
50.0 |
5.223 |
4.81e-05 |
35.143 |
| DEMetro_Z |
2.1 |
4.597 |
0.000194 |
18.740 |
| DEMetro_Z |
3.0 |
4.712 |
0.000149 |
16.871 |
| DEMetro_Z |
4.0 |
5.137 |
5.74e-05 |
19.505 |
| DEMetro_Z |
10.0 |
8.746 |
4.06e-08 |
29.924 |
| DEMetro_Z |
50.0 |
4.951 |
8.81e-05 |
29.358 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
2.475
|
0.0229
|
0.553
|
| DEMetro_Z_vs_SMC |
1
|
3.966
|
0.000829
|
0.887
|
| DEMetro_Z_vs_SMC |
2
|
5.126
|
6e-05
|
1.146
|
| DEMetro_Z_vs_SMC |
3
|
8.864
|
3.54e-08
|
1.982
|
| DEMetro_Z_vs_SMC |
4
|
4.875
|
0.000105
|
1.090
|
| HMC_vs_Metro |
0
|
3.410
|
0.00294
|
0.762
|
| HMC_vs_Metro |
1
|
0.084
|
0.934
|
0.019
|
| HMC_vs_Metro |
2
|
0.102
|
0.92
|
0.023
|
| HMC_vs_Metro |
3
|
-1.553
|
0.137
|
-0.347
|
| HMC_vs_Metro |
4
|
0.793
|
0.438
|
0.177
|
| Metro_vs_DEMetro_Z |
0
|
-3.557
|
0.00211
|
-0.795
|
| Metro_vs_DEMetro_Z |
1
|
-0.799
|
0.434
|
-0.179
|
| Metro_vs_DEMetro_Z |
2
|
-0.391
|
0.7
|
-0.087
|
| Metro_vs_DEMetro_Z |
3
|
0.217
|
0.83
|
0.049
|
| Metro_vs_DEMetro_Z |
4
|
0.794
|
0.437
|
0.178
|
| HMC_vs_SMC |
0
|
0.869
|
0.396
|
0.194
|
| HMC_vs_SMC |
1
|
4.351
|
0.000344
|
0.973
|
| HMC_vs_SMC |
2
|
6.329
|
4.5e-06
|
1.415
|
| HMC_vs_SMC |
3
|
4.401
|
0.000307
|
0.984
|
| HMC_vs_SMC |
4
|
5.068
|
6.83e-05
|
1.133
|
| Metro_vs_SMC |
0
|
-2.448
|
0.0242
|
-0.547
|
| Metro_vs_SMC |
1
|
4.530
|
0.000229
|
1.013
|
| Metro_vs_SMC |
2
|
4.380
|
0.000322
|
0.979
|
| Metro_vs_SMC |
3
|
5.170
|
5.45e-05
|
1.156
|
| Metro_vs_SMC |
4
|
5.163
|
5.53e-05
|
1.154
|
| HMC_vs_DEMetro_Z |
0
|
-2.001
|
0.0599
|
-0.447
|
| HMC_vs_DEMetro_Z |
1
|
-0.517
|
0.611
|
-0.116
|
| HMC_vs_DEMetro_Z |
2
|
-0.344
|
0.735
|
-0.077
|
| HMC_vs_DEMetro_Z |
3
|
-1.032
|
0.315
|
-0.231
|
| HMC_vs_DEMetro_Z |
4
|
1.346
|
0.194
|
0.301
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.073 |
0.009 |
0.006 |
11.037 |
| HMC |
3.0 |
0.131 |
0.014 |
0.008 |
14.419 |
| HMC |
4.0 |
0.183 |
0.013 |
0.010 |
17.764 |
| HMC |
10.0 |
0.200 |
0.014 |
0.008 |
23.427 |
| HMC |
50.0 |
0.275 |
0.011 |
0.007 |
39.589 |
| SMC |
2.1 |
0.060 |
0.009 |
0.006 |
8.757 |
| SMC |
3.0 |
0.032 |
0.014 |
0.008 |
2.266 |
| SMC |
4.0 |
0.015 |
0.013 |
0.010 |
0.241 |
| SMC |
10.0 |
0.012 |
0.014 |
0.008 |
-0.238 |
| SMC |
50.0 |
0.011 |
0.011 |
0.007 |
0.090 |
| Metro |
2.1 |
0.037 |
0.009 |
0.006 |
4.752 |
| Metro |
3.0 |
0.128 |
0.014 |
0.008 |
14.080 |
| Metro |
4.0 |
0.178 |
0.013 |
0.010 |
17.260 |
| Metro |
10.0 |
0.263 |
0.014 |
0.008 |
31.428 |
| Metro |
50.0 |
0.245 |
0.011 |
0.007 |
35.143 |
| DEMetro_Z |
2.1 |
0.117 |
0.009 |
0.006 |
18.740 |
| DEMetro_Z |
3.0 |
0.151 |
0.014 |
0.008 |
16.871 |
| DEMetro_Z |
4.0 |
0.199 |
0.013 |
0.010 |
19.505 |
| DEMetro_Z |
10.0 |
0.251 |
0.014 |
0.008 |
29.924 |
| DEMetro_Z |
50.0 |
0.206 |
0.011 |
0.007 |
29.358 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.869 |
1.08e-05 |
12.270 |
| HMC |
3.0 |
5.338 |
3.55e-05 |
12.913 |
| HMC |
4.0 |
6.494 |
2.81e-06 |
12.620 |
| HMC |
10.0 |
20.410 |
1.79e-14 |
65.467 |
| HMC |
50.0 |
284.822 |
5.26e-64 |
96.381 |
| SMC |
2.1 |
5.062 |
6.37e-05 |
9.563 |
| SMC |
3.0 |
2.693 |
0.0116 |
1.252 |
| SMC |
4.0 |
0.640 |
0.526 |
0.195 |
| SMC |
10.0 |
-2.368 |
0.0237 |
-0.646 |
| SMC |
50.0 |
-0.132 |
0.896 |
-0.051 |
| Metro |
2.1 |
4.138 |
0.000447 |
3.689 |
| Metro |
3.0 |
3.132 |
0.00545 |
10.812 |
| Metro |
4.0 |
3.377 |
0.00315 |
15.272 |
| Metro |
10.0 |
12.217 |
1.82e-10 |
60.619 |
| Metro |
50.0 |
249.857 |
1.52e-57 |
96.327 |
| DEMetro_Z |
2.1 |
5.183 |
5.07e-05 |
13.871 |
| DEMetro_Z |
3.0 |
3.577 |
0.002 |
15.532 |
| DEMetro_Z |
4.0 |
4.966 |
8.5e-05 |
28.899 |
| DEMetro_Z |
10.0 |
5.898 |
1.11e-05 |
42.872 |
| DEMetro_Z |
50.0 |
7.601 |
3.53e-07 |
70.154 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.469
|
0.644
|
-0.105
|
| HMC_vs_DEMetro_Z |
1
|
-0.583
|
0.567
|
-0.130
|
| HMC_vs_DEMetro_Z |
2
|
-2.833
|
0.0106
|
-0.633
|
| HMC_vs_DEMetro_Z |
3
|
2.618
|
0.0169
|
0.585
|
| HMC_vs_DEMetro_Z |
4
|
2.872
|
0.00976
|
0.642
|
| Metro_vs_SMC |
0
|
-3.169
|
0.00505
|
-0.709
|
| Metro_vs_SMC |
1
|
2.695
|
0.0143
|
0.603
|
| Metro_vs_SMC |
2
|
3.357
|
0.00331
|
0.751
|
| Metro_vs_SMC |
3
|
12.388
|
1.51e-10
|
2.770
|
| Metro_vs_SMC |
4
|
254.702
|
4.89e-35
|
56.953
|
| Metro_vs_DEMetro_Z |
0
|
-3.846
|
0.00109
|
-0.860
|
| Metro_vs_DEMetro_Z |
1
|
-0.768
|
0.452
|
-0.172
|
| Metro_vs_DEMetro_Z |
2
|
-1.792
|
0.0891
|
-0.401
|
| Metro_vs_DEMetro_Z |
3
|
1.965
|
0.0642
|
0.439
|
| Metro_vs_DEMetro_Z |
4
|
2.887
|
0.00945
|
0.646
|
| HMC_vs_Metro |
0
|
3.399
|
0.00301
|
0.760
|
| HMC_vs_Metro |
1
|
0.519
|
0.61
|
0.116
|
| HMC_vs_Metro |
2
|
-0.542
|
0.594
|
-0.121
|
| HMC_vs_Metro |
3
|
0.825
|
0.419
|
0.185
|
| HMC_vs_Metro |
4
|
0.369
|
0.717
|
0.082
|
| HMC_vs_SMC |
0
|
0.806
|
0.43
|
0.180
|
| HMC_vs_SMC |
1
|
4.769
|
0.000134
|
1.066
|
| HMC_vs_SMC |
2
|
6.169
|
6.28e-06
|
1.379
|
| HMC_vs_SMC |
3
|
20.889
|
1.44e-14
|
4.671
|
| HMC_vs_SMC |
4
|
273.259
|
1.29e-35
|
61.103
|
| DEMetro_Z_vs_SMC |
0
|
1.229
|
0.234
|
0.275
|
| DEMetro_Z_vs_SMC |
1
|
3.307
|
0.00371
|
0.739
|
| DEMetro_Z_vs_SMC |
2
|
4.923
|
9.43e-05
|
1.101
|
| DEMetro_Z_vs_SMC |
3
|
5.998
|
9.01e-06
|
1.341
|
| DEMetro_Z_vs_SMC |
4
|
7.650
|
3.23e-07
|
1.711
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.915 |
0.086 |
0.068 |
12.270 |
| HMC |
3.0 |
1.230 |
0.125 |
0.086 |
12.913 |
| HMC |
4.0 |
1.279 |
0.110 |
0.093 |
12.620 |
| HMC |
10.0 |
5.334 |
0.126 |
0.080 |
65.467 |
| HMC |
50.0 |
5.678 |
0.089 |
0.058 |
96.381 |
| SMC |
2.1 |
0.732 |
0.086 |
0.068 |
9.563 |
| SMC |
3.0 |
0.232 |
0.125 |
0.086 |
1.252 |
| SMC |
4.0 |
0.129 |
0.110 |
0.093 |
0.195 |
| SMC |
10.0 |
0.075 |
0.126 |
0.080 |
-0.646 |
| SMC |
50.0 |
0.086 |
0.089 |
0.058 |
-0.051 |
| Metro |
2.1 |
0.335 |
0.086 |
0.068 |
3.689 |
| Metro |
3.0 |
1.050 |
0.125 |
0.086 |
10.812 |
| Metro |
4.0 |
1.524 |
0.110 |
0.093 |
15.272 |
| Metro |
10.0 |
4.948 |
0.126 |
0.080 |
60.619 |
| Metro |
50.0 |
5.675 |
0.089 |
0.058 |
96.327 |
| DEMetro_Z |
2.1 |
1.024 |
0.086 |
0.068 |
13.871 |
| DEMetro_Z |
3.0 |
1.455 |
0.125 |
0.086 |
15.532 |
| DEMetro_Z |
4.0 |
2.786 |
0.110 |
0.093 |
28.899 |
| DEMetro_Z |
10.0 |
3.537 |
0.126 |
0.080 |
42.872 |
| DEMetro_Z |
50.0 |
4.157 |
0.089 |
0.058 |
70.154 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.287 |
0.213 |
-0.293 |
| HMC |
3.0 |
3.616 |
0.00181 |
9.325 |
| HMC |
4.0 |
3.847 |
0.00107 |
13.753 |
| HMC |
10.0 |
17.532 |
3.39e-13 |
201.278 |
| HMC |
50.0 |
856.397 |
1.1e-81 |
253.958 |
| SMC |
2.1 |
-1.554 |
0.136 |
-0.348 |
| SMC |
3.0 |
0.455 |
0.652 |
0.204 |
| SMC |
4.0 |
-0.667 |
0.509 |
-0.205 |
| SMC |
10.0 |
-0.607 |
0.549 |
-0.155 |
| SMC |
50.0 |
-0.861 |
0.397 |
-0.219 |
| Metro |
2.1 |
-1.290 |
0.211 |
-0.300 |
| Metro |
3.0 |
2.395 |
0.027 |
12.462 |
| Metro |
4.0 |
2.275 |
0.0346 |
34.020 |
| Metro |
10.0 |
10.677 |
1.81e-09 |
185.080 |
| Metro |
50.0 |
858.300 |
1.29e-81 |
253.915 |
| DEMetro_Z |
2.1 |
-1.393 |
0.18 |
-0.312 |
| DEMetro_Z |
3.0 |
2.292 |
0.0335 |
20.640 |
| DEMetro_Z |
4.0 |
3.926 |
0.000906 |
88.950 |
| DEMetro_Z |
10.0 |
5.465 |
2.84e-05 |
129.224 |
| DEMetro_Z |
50.0 |
6.797 |
1.72e-06 |
178.852 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.424
|
0.171
|
0.318
|
| HMC_vs_SMC |
1
|
3.490
|
0.00245
|
0.780
|
| HMC_vs_SMC |
2
|
3.819
|
0.00116
|
0.854
|
| HMC_vs_SMC |
3
|
17.579
|
3.28e-13
|
3.931
|
| HMC_vs_SMC |
4
|
1609.079
|
3.02e-50
|
359.801
|
| Metro_vs_DEMetro_Z |
0
|
0.223
|
0.826
|
0.050
|
| Metro_vs_DEMetro_Z |
1
|
-0.734
|
0.472
|
-0.164
|
| Metro_vs_DEMetro_Z |
2
|
-2.010
|
0.0588
|
-0.449
|
| Metro_vs_DEMetro_Z |
3
|
1.851
|
0.0798
|
0.414
|
| Metro_vs_DEMetro_Z |
4
|
2.847
|
0.0103
|
0.637
|
| HMC_vs_Metro |
0
|
0.105
|
0.918
|
0.023
|
| HMC_vs_Metro |
1
|
-0.567
|
0.577
|
-0.127
|
| HMC_vs_Metro |
2
|
-1.377
|
0.185
|
-0.308
|
| HMC_vs_Metro |
3
|
0.829
|
0.417
|
0.185
|
| HMC_vs_Metro |
4
|
0.823
|
0.421
|
0.184
|
| HMC_vs_DEMetro_Z |
0
|
0.444
|
0.662
|
0.099
|
| HMC_vs_DEMetro_Z |
1
|
-1.278
|
0.217
|
-0.286
|
| HMC_vs_DEMetro_Z |
2
|
-3.482
|
0.0025
|
-0.779
|
| HMC_vs_DEMetro_Z |
3
|
2.497
|
0.0219
|
0.558
|
| HMC_vs_DEMetro_Z |
4
|
2.849
|
0.0103
|
0.637
|
| Metro_vs_SMC |
0
|
0.835
|
0.414
|
0.187
|
| Metro_vs_SMC |
1
|
2.349
|
0.0298
|
0.525
|
| Metro_vs_SMC |
2
|
2.305
|
0.0326
|
0.515
|
| Metro_vs_SMC |
3
|
10.693
|
1.77e-09
|
2.391
|
| Metro_vs_SMC |
4
|
1715.112
|
8.98e-51
|
383.511
|
| DEMetro_Z_vs_SMC |
0
|
2.682
|
0.0147
|
0.600
|
| DEMetro_Z_vs_SMC |
1
|
2.311
|
0.0322
|
0.517
|
| DEMetro_Z_vs_SMC |
2
|
3.921
|
0.000918
|
0.877
|
| DEMetro_Z_vs_SMC |
3
|
5.474
|
2.79e-05
|
1.224
|
| DEMetro_Z_vs_SMC |
4
|
6.802
|
1.71e-06
|
1.521
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.033 |
17.896 |
40.526 |
-0.293 |
| HMC |
3.0 |
3.677 |
0.600 |
0.330 |
9.325 |
| HMC |
4.0 |
3.198 |
0.356 |
0.207 |
13.753 |
| HMC |
10.0 |
42.046 |
0.202 |
0.208 |
201.278 |
| HMC |
50.0 |
45.267 |
0.210 |
0.177 |
253.958 |
| SMC |
2.1 |
3.774 |
17.896 |
40.526 |
-0.348 |
| SMC |
3.0 |
0.667 |
0.600 |
0.330 |
0.204 |
| SMC |
4.0 |
0.314 |
0.356 |
0.207 |
-0.205 |
| SMC |
10.0 |
0.170 |
0.202 |
0.208 |
-0.155 |
| SMC |
50.0 |
0.171 |
0.210 |
0.177 |
-0.219 |
| Metro |
2.1 |
5.735 |
17.896 |
40.526 |
-0.300 |
| Metro |
3.0 |
4.712 |
0.600 |
0.330 |
12.462 |
| Metro |
4.0 |
7.386 |
0.356 |
0.207 |
34.020 |
| Metro |
10.0 |
38.679 |
0.202 |
0.208 |
185.080 |
| Metro |
50.0 |
45.259 |
0.210 |
0.177 |
253.915 |
| DEMetro_Z |
2.1 |
5.240 |
17.896 |
40.526 |
-0.312 |
| DEMetro_Z |
3.0 |
7.410 |
0.600 |
0.330 |
20.640 |
| DEMetro_Z |
4.0 |
18.738 |
0.356 |
0.207 |
88.950 |
| DEMetro_Z |
10.0 |
27.067 |
0.202 |
0.208 |
129.224 |
| DEMetro_Z |
50.0 |
31.942 |
0.210 |
0.177 |
178.852 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.857 |
1.02e-05 |
8.663 |
| HMC |
3.0 |
5.305 |
3.84e-05 |
13.237 |
| HMC |
4.0 |
6.379 |
3.66e-06 |
13.647 |
| HMC |
10.0 |
18.639 |
1.02e-13 |
76.667 |
| HMC |
50.0 |
61.039 |
6.57e-24 |
102.675 |
| SMC |
2.1 |
5.370 |
2.99e-05 |
7.753 |
| SMC |
3.0 |
3.090 |
0.00429 |
1.399 |
| SMC |
4.0 |
0.243 |
0.81 |
0.076 |
| SMC |
10.0 |
-2.508 |
0.0171 |
-0.683 |
| SMC |
50.0 |
-0.287 |
0.776 |
-0.110 |
| Metro |
2.1 |
3.983 |
0.000628 |
3.277 |
| Metro |
3.0 |
3.232 |
0.00436 |
11.278 |
| Metro |
4.0 |
3.347 |
0.00337 |
15.992 |
| Metro |
10.0 |
11.866 |
3.03e-10 |
72.387 |
| Metro |
50.0 |
55.600 |
5.46e-23 |
104.811 |
| DEMetro_Z |
2.1 |
5.140 |
5.38e-05 |
9.984 |
| DEMetro_Z |
3.0 |
3.905 |
0.000942 |
15.341 |
| DEMetro_Z |
4.0 |
4.957 |
8.69e-05 |
31.966 |
| DEMetro_Z |
10.0 |
5.906 |
1.09e-05 |
48.056 |
| DEMetro_Z |
50.0 |
7.514 |
4.17e-07 |
76.192 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.318
|
0.00361
|
-0.742
|
| Metro_vs_DEMetro_Z |
1
|
-0.699
|
0.493
|
-0.156
|
| Metro_vs_DEMetro_Z |
2
|
-1.940
|
0.0673
|
-0.434
|
| Metro_vs_DEMetro_Z |
3
|
2.476
|
0.0229
|
0.554
|
| Metro_vs_DEMetro_Z |
4
|
2.681
|
0.0148
|
0.599
|
| DEMetro_Z_vs_SMC |
0
|
0.859
|
0.401
|
0.192
|
| DEMetro_Z_vs_SMC |
1
|
3.547
|
0.00215
|
0.793
|
| DEMetro_Z_vs_SMC |
2
|
4.933
|
9.24e-05
|
1.103
|
| DEMetro_Z_vs_SMC |
3
|
6.000
|
8.98e-06
|
1.342
|
| DEMetro_Z_vs_SMC |
4
|
7.553
|
3.9e-07
|
1.689
|
| HMC_vs_DEMetro_Z |
0
|
-0.536
|
0.598
|
-0.120
|
| HMC_vs_DEMetro_Z |
1
|
-0.481
|
0.636
|
-0.108
|
| HMC_vs_DEMetro_Z |
2
|
-2.917
|
0.00885
|
-0.652
|
| HMC_vs_DEMetro_Z |
3
|
2.959
|
0.00806
|
0.662
|
| HMC_vs_DEMetro_Z |
4
|
2.662
|
0.0154
|
0.595
|
| HMC_vs_Metro |
0
|
2.853
|
0.0102
|
0.638
|
| HMC_vs_Metro |
1
|
0.480
|
0.637
|
0.107
|
| HMC_vs_Metro |
2
|
-0.451
|
0.657
|
-0.101
|
| HMC_vs_Metro |
3
|
0.629
|
0.537
|
0.141
|
| HMC_vs_Metro |
4
|
-1.076
|
0.296
|
-0.241
|
| HMC_vs_SMC |
0
|
0.376
|
0.711
|
0.084
|
| HMC_vs_SMC |
1
|
4.662
|
0.00017
|
1.042
|
| HMC_vs_SMC |
2
|
6.113
|
7.07e-06
|
1.367
|
| HMC_vs_SMC |
3
|
18.928
|
8.65e-14
|
4.232
|
| HMC_vs_SMC |
4
|
66.903
|
5.07e-24
|
14.960
|
| Metro_vs_SMC |
0
|
-2.965
|
0.00795
|
-0.663
|
| Metro_vs_SMC |
1
|
2.756
|
0.0126
|
0.616
|
| Metro_vs_SMC |
2
|
3.375
|
0.00318
|
0.755
|
| Metro_vs_SMC |
3
|
12.007
|
2.56e-10
|
2.685
|
| Metro_vs_SMC |
4
|
55.526
|
1.72e-22
|
12.416
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.908 |
0.180 |
0.084 |
8.663 |
| HMC |
3.0 |
1.148 |
0.153 |
0.075 |
13.237 |
| HMC |
4.0 |
1.197 |
0.136 |
0.078 |
13.647 |
| HMC |
10.0 |
4.853 |
0.132 |
0.062 |
76.667 |
| HMC |
50.0 |
5.012 |
0.101 |
0.048 |
102.675 |
| SMC |
2.1 |
0.831 |
0.180 |
0.084 |
7.753 |
| SMC |
3.0 |
0.258 |
0.153 |
0.075 |
1.399 |
| SMC |
4.0 |
0.142 |
0.136 |
0.078 |
0.076 |
| SMC |
10.0 |
0.090 |
0.132 |
0.062 |
-0.683 |
| SMC |
50.0 |
0.096 |
0.101 |
0.048 |
-0.110 |
| Metro |
2.1 |
0.455 |
0.180 |
0.084 |
3.277 |
| Metro |
3.0 |
1.001 |
0.153 |
0.075 |
11.278 |
| Metro |
4.0 |
1.380 |
0.136 |
0.078 |
15.992 |
| Metro |
10.0 |
4.590 |
0.132 |
0.062 |
72.387 |
| Metro |
50.0 |
5.114 |
0.101 |
0.048 |
104.811 |
| DEMetro_Z |
2.1 |
1.019 |
0.180 |
0.084 |
9.984 |
| DEMetro_Z |
3.0 |
1.307 |
0.153 |
0.075 |
15.341 |
| DEMetro_Z |
4.0 |
2.622 |
0.136 |
0.078 |
31.966 |
| DEMetro_Z |
10.0 |
3.091 |
0.132 |
0.062 |
48.056 |
| DEMetro_Z |
50.0 |
3.745 |
0.101 |
0.048 |
76.192 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.544 |
2.27e-05 |
14.662 |
| HMC |
3.0 |
5.043 |
6.99e-05 |
14.993 |
| HMC |
4.0 |
6.319 |
4.17e-06 |
14.011 |
| HMC |
10.0 |
20.508 |
1.69e-14 |
71.187 |
| HMC |
50.0 |
110.039 |
1.41e-31 |
91.697 |
| SMC |
2.1 |
5.272 |
4.06e-05 |
11.389 |
| SMC |
3.0 |
2.796 |
0.00909 |
1.333 |
| SMC |
4.0 |
0.245 |
0.808 |
0.076 |
| SMC |
10.0 |
-2.440 |
0.02 |
-0.669 |
| SMC |
50.0 |
-0.225 |
0.824 |
-0.085 |
| Metro |
2.1 |
4.473 |
0.000194 |
3.820 |
| Metro |
3.0 |
3.077 |
0.00618 |
12.729 |
| Metro |
4.0 |
3.400 |
0.00299 |
15.957 |
| Metro |
10.0 |
12.182 |
1.92e-10 |
66.230 |
| Metro |
50.0 |
117.022 |
1.24e-32 |
91.872 |
| DEMetro_Z |
2.1 |
4.685 |
0.000158 |
16.424 |
| DEMetro_Z |
3.0 |
3.680 |
0.00158 |
18.245 |
| DEMetro_Z |
4.0 |
5.047 |
7.1e-05 |
31.077 |
| DEMetro_Z |
10.0 |
5.966 |
9.59e-06 |
47.214 |
| DEMetro_Z |
50.0 |
7.661 |
3.14e-07 |
66.771 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
1.144
|
0.267
|
0.256
|
| DEMetro_Z_vs_SMC |
1
|
3.418
|
0.00288
|
0.764
|
| DEMetro_Z_vs_SMC |
2
|
5.019
|
7.63e-05
|
1.122
|
| DEMetro_Z_vs_SMC |
3
|
6.060
|
7.91e-06
|
1.355
|
| DEMetro_Z_vs_SMC |
4
|
7.701
|
2.94e-07
|
1.722
|
| HMC_vs_Metro |
0
|
3.747
|
0.00137
|
0.838
|
| HMC_vs_Metro |
1
|
0.460
|
0.651
|
0.103
|
| HMC_vs_Metro |
2
|
-0.382
|
0.707
|
-0.085
|
| HMC_vs_Metro |
3
|
0.773
|
0.449
|
0.173
|
| HMC_vs_Metro |
4
|
-0.199
|
0.844
|
-0.045
|
| Metro_vs_DEMetro_Z |
0
|
-3.834
|
0.00112
|
-0.857
|
| Metro_vs_DEMetro_Z |
1
|
-0.772
|
0.45
|
-0.173
|
| Metro_vs_DEMetro_Z |
2
|
-1.903
|
0.0723
|
-0.425
|
| Metro_vs_DEMetro_Z |
3
|
1.928
|
0.069
|
0.431
|
| Metro_vs_DEMetro_Z |
4
|
2.938
|
0.00844
|
0.657
|
| HMC_vs_SMC |
0
|
0.813
|
0.426
|
0.182
|
| HMC_vs_SMC |
1
|
4.542
|
0.000223
|
1.016
|
| HMC_vs_SMC |
2
|
6.086
|
7.49e-06
|
1.361
|
| HMC_vs_SMC |
3
|
20.967
|
1.35e-14
|
4.688
|
| HMC_vs_SMC |
4
|
110.324
|
3.87e-28
|
24.669
|
| Metro_vs_SMC |
0
|
-3.573
|
0.00203
|
-0.799
|
| Metro_vs_SMC |
1
|
2.698
|
0.0142
|
0.603
|
| Metro_vs_SMC |
2
|
3.408
|
0.00295
|
0.762
|
| Metro_vs_SMC |
3
|
12.371
|
1.55e-10
|
2.766
|
| Metro_vs_SMC |
4
|
116.039
|
1.49e-28
|
25.947
|
| HMC_vs_DEMetro_Z |
0
|
-0.399
|
0.694
|
-0.089
|
| HMC_vs_DEMetro_Z |
1
|
-0.628
|
0.538
|
-0.140
|
| HMC_vs_DEMetro_Z |
2
|
-2.805
|
0.0113
|
-0.627
|
| HMC_vs_DEMetro_Z |
3
|
2.538
|
0.0201
|
0.567
|
| HMC_vs_DEMetro_Z |
4
|
2.816
|
0.011
|
0.630
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.093 |
0.009 |
0.006 |
14.662 |
| HMC |
3.0 |
0.136 |
0.014 |
0.008 |
14.993 |
| HMC |
4.0 |
0.147 |
0.013 |
0.010 |
14.011 |
| HMC |
10.0 |
0.579 |
0.014 |
0.008 |
71.187 |
| HMC |
50.0 |
0.622 |
0.011 |
0.007 |
91.697 |
| SMC |
2.1 |
0.075 |
0.009 |
0.006 |
11.389 |
| SMC |
3.0 |
0.024 |
0.014 |
0.008 |
1.333 |
| SMC |
4.0 |
0.014 |
0.013 |
0.010 |
0.076 |
| SMC |
10.0 |
0.008 |
0.014 |
0.008 |
-0.669 |
| SMC |
50.0 |
0.010 |
0.011 |
0.007 |
-0.085 |
| Metro |
2.1 |
0.031 |
0.009 |
0.006 |
3.820 |
| Metro |
3.0 |
0.117 |
0.014 |
0.008 |
12.729 |
| Metro |
4.0 |
0.165 |
0.013 |
0.010 |
15.957 |
| Metro |
10.0 |
0.540 |
0.014 |
0.008 |
66.230 |
| Metro |
50.0 |
0.624 |
0.011 |
0.007 |
91.872 |
| DEMetro_Z |
2.1 |
0.104 |
0.009 |
0.006 |
16.424 |
| DEMetro_Z |
3.0 |
0.162 |
0.014 |
0.008 |
18.245 |
| DEMetro_Z |
4.0 |
0.310 |
0.013 |
0.010 |
31.077 |
| DEMetro_Z |
10.0 |
0.389 |
0.014 |
0.008 |
47.214 |
| DEMetro_Z |
50.0 |
0.456 |
0.011 |
0.007 |
66.771 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Dimension_and_high_Correlation
(MvStudentT,
nu,
20 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.381 |
0.00282 |
3.383 |
| HMC |
3.0 |
3.768 |
0.00123 |
5.938 |
| HMC |
4.0 |
4.957 |
7e-05 |
5.511 |
| HMC |
10.0 |
5.534 |
1.25e-05 |
3.991 |
| HMC |
50.0 |
3.368 |
0.00274 |
2.664 |
| SMC |
2.1 |
78.276 |
2.45e-25 |
700.210 |
| SMC |
3.0 |
12.837 |
5.53e-11 |
23.673 |
| SMC |
4.0 |
15.311 |
3.32e-12 |
51.236 |
| SMC |
10.0 |
6.196 |
5.89e-06 |
44.674 |
| SMC |
50.0 |
13.264 |
4.68e-11 |
352.825 |
| Metro |
2.1 |
2.747 |
0.0128 |
608.155 |
| Metro |
3.0 |
4.287 |
0.000398 |
108.732 |
| Metro |
4.0 |
4.540 |
0.000224 |
227.346 |
| Metro |
10.0 |
6.633 |
2.4e-06 |
80.294 |
| Metro |
50.0 |
4.982 |
8.26e-05 |
51.647 |
| DEMetro_Z |
2.1 |
14.839 |
6.65e-12 |
937.201 |
| DEMetro_Z |
3.0 |
8.756 |
4.26e-08 |
209.731 |
| DEMetro_Z |
4.0 |
6.711 |
2.05e-06 |
349.114 |
| DEMetro_Z |
10.0 |
7.000 |
1.15e-06 |
169.990 |
| DEMetro_Z |
50.0 |
7.393 |
5.3e-07 |
196.491 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-14.822
|
6.79e-12
|
-3.314
|
| HMC_vs_DEMetro_Z |
1
|
-8.535
|
6.33e-08
|
-1.908
|
| HMC_vs_DEMetro_Z |
2
|
-6.614
|
2.5e-06
|
-1.479
|
| HMC_vs_DEMetro_Z |
3
|
-6.767
|
1.83e-06
|
-1.513
|
| HMC_vs_DEMetro_Z |
4
|
-7.284
|
6.56e-07
|
-1.629
|
| Metro_vs_SMC |
0
|
-0.415
|
0.683
|
-0.093
|
| Metro_vs_SMC |
1
|
3.403
|
0.00299
|
0.761
|
| Metro_vs_SMC |
2
|
3.507
|
0.00236
|
0.784
|
| Metro_vs_SMC |
3
|
2.314
|
0.032
|
0.517
|
| Metro_vs_SMC |
4
|
-9.220
|
1.91e-08
|
-2.062
|
| Metro_vs_DEMetro_Z |
0
|
-1.358
|
0.19
|
-0.304
|
| Metro_vs_DEMetro_Z |
1
|
-2.493
|
0.0221
|
-0.557
|
| Metro_vs_DEMetro_Z |
2
|
-1.700
|
0.105
|
-0.380
|
| Metro_vs_DEMetro_Z |
3
|
-3.513
|
0.00233
|
-0.786
|
| Metro_vs_DEMetro_Z |
4
|
-4.889
|
0.000102
|
-1.093
|
| HMC_vs_Metro |
0
|
-2.730
|
0.0133
|
-0.611
|
| HMC_vs_Metro |
1
|
-4.159
|
0.000533
|
-0.930
|
| HMC_vs_Metro |
2
|
-4.435
|
0.000284
|
-0.992
|
| HMC_vs_Metro |
3
|
-6.444
|
3.54e-06
|
-1.441
|
| HMC_vs_Metro |
4
|
-4.700
|
0.000156
|
-1.051
|
| HMC_vs_SMC |
0
|
-77.094
|
3.46e-25
|
-17.239
|
| HMC_vs_SMC |
1
|
-10.171
|
4e-09
|
-2.274
|
| HMC_vs_SMC |
2
|
-13.094
|
5.86e-11
|
-2.928
|
| HMC_vs_SMC |
3
|
-5.602
|
2.11e-05
|
-1.253
|
| HMC_vs_SMC |
4
|
-13.128
|
5.6e-11
|
-2.936
|
| DEMetro_Z_vs_SMC |
0
|
3.665
|
0.00165
|
0.819
|
| DEMetro_Z_vs_SMC |
1
|
7.805
|
2.41e-07
|
1.745
|
| DEMetro_Z_vs_SMC |
2
|
5.803
|
1.37e-05
|
1.298
|
| DEMetro_Z_vs_SMC |
3
|
4.585
|
0.000202
|
1.025
|
| DEMetro_Z_vs_SMC |
4
|
-4.870
|
0.000106
|
-1.089
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.188 |
0.069 |
0.035 |
3.383 |
| HMC |
3.0 |
0.145 |
0.032 |
0.019 |
5.938 |
| HMC |
4.0 |
0.106 |
0.026 |
0.015 |
5.511 |
| HMC |
10.0 |
0.076 |
0.021 |
0.014 |
3.991 |
| HMC |
50.0 |
0.050 |
0.019 |
0.012 |
2.664 |
| SMC |
2.1 |
24.649 |
0.069 |
0.035 |
700.210 |
| SMC |
3.0 |
0.480 |
0.032 |
0.019 |
23.673 |
| SMC |
4.0 |
0.769 |
0.026 |
0.015 |
51.236 |
| SMC |
10.0 |
0.637 |
0.021 |
0.014 |
44.674 |
| SMC |
50.0 |
4.182 |
0.019 |
0.012 |
352.825 |
| Metro |
2.1 |
21.417 |
0.069 |
0.035 |
608.155 |
| Metro |
3.0 |
2.086 |
0.032 |
0.019 |
108.732 |
| Metro |
4.0 |
3.323 |
0.026 |
0.015 |
227.346 |
| Metro |
10.0 |
1.128 |
0.021 |
0.014 |
80.294 |
| Metro |
50.0 |
0.628 |
0.019 |
0.012 |
51.647 |
| DEMetro_Z |
2.1 |
32.968 |
0.069 |
0.035 |
937.201 |
| DEMetro_Z |
3.0 |
3.994 |
0.032 |
0.019 |
209.731 |
| DEMetro_Z |
4.0 |
5.089 |
0.026 |
0.015 |
349.114 |
| DEMetro_Z |
10.0 |
2.365 |
0.021 |
0.014 |
169.990 |
| DEMetro_Z |
50.0 |
2.337 |
0.019 |
0.012 |
196.491 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.249 |
0.805 |
0.065 |
| HMC |
3.0 |
3.081 |
0.00532 |
2.273 |
| HMC |
4.0 |
4.161 |
0.000316 |
2.401 |
| HMC |
10.0 |
4.627 |
0.000155 |
5.454 |
| HMC |
50.0 |
4.354 |
0.00029 |
4.868 |
| SMC |
2.1 |
231.787 |
1.44e-34 |
711.610 |
| SMC |
3.0 |
264.712 |
1.83e-35 |
1383.760 |
| SMC |
4.0 |
200.568 |
4.52e-33 |
4616.389 |
| SMC |
10.0 |
35.532 |
7.66e-19 |
16720.900 |
| SMC |
50.0 |
110.292 |
3.89e-28 |
29098.775 |
| Metro |
2.1 |
1.612 |
0.123 |
714.282 |
| Metro |
3.0 |
2.649 |
0.0158 |
251.626 |
| Metro |
4.0 |
3.509 |
0.00235 |
550.263 |
| Metro |
10.0 |
5.339 |
3.75e-05 |
412.503 |
| Metro |
50.0 |
4.065 |
0.00066 |
76.597 |
| DEMetro_Z |
2.1 |
9.721 |
8.27e-09 |
210.856 |
| DEMetro_Z |
3.0 |
11.431 |
5.86e-10 |
420.084 |
| DEMetro_Z |
4.0 |
10.031 |
5.01e-09 |
1308.248 |
| DEMetro_Z |
10.0 |
8.850 |
3.63e-08 |
1959.442 |
| DEMetro_Z |
50.0 |
7.573 |
3.75e-07 |
1328.110 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-229.623
|
3.5e-34
|
-51.345
|
| HMC_vs_SMC |
1
|
-274.074
|
1.21e-35
|
-61.285
|
| HMC_vs_SMC |
2
|
-200.092
|
4.78e-33
|
-44.742
|
| HMC_vs_SMC |
3
|
-35.495
|
7.82e-19
|
-7.937
|
| HMC_vs_SMC |
4
|
-110.152
|
3.99e-28
|
-24.631
|
| Metro_vs_DEMetro_Z |
0
|
1.148
|
0.265
|
0.257
|
| Metro_vs_DEMetro_Z |
1
|
-1.727
|
0.1
|
-0.386
|
| Metro_vs_DEMetro_Z |
2
|
-3.456
|
0.00265
|
-0.773
|
| Metro_vs_DEMetro_Z |
3
|
-6.045
|
8.17e-06
|
-1.352
|
| Metro_vs_DEMetro_Z |
4
|
-7.151
|
8.51e-07
|
-1.599
|
| HMC_vs_Metro |
0
|
-1.612
|
0.123
|
-0.360
|
| HMC_vs_Metro |
1
|
-2.624
|
0.0167
|
-0.587
|
| HMC_vs_Metro |
2
|
-3.491
|
0.00244
|
-0.781
|
| HMC_vs_Metro |
3
|
-5.302
|
4.07e-05
|
-1.186
|
| HMC_vs_Metro |
4
|
-3.819
|
0.00116
|
-0.854
|
| HMC_vs_DEMetro_Z |
0
|
-9.715
|
8.37e-09
|
-2.172
|
| HMC_vs_DEMetro_Z |
1
|
-11.327
|
6.83e-10
|
-2.533
|
| HMC_vs_DEMetro_Z |
2
|
-10.015
|
5.14e-09
|
-2.239
|
| HMC_vs_DEMetro_Z |
3
|
-8.837
|
3.71e-08
|
-1.976
|
| HMC_vs_DEMetro_Z |
4
|
-7.556
|
3.87e-07
|
-1.690
|
| Metro_vs_SMC |
0
|
0.006
|
0.995
|
0.001
|
| Metro_vs_SMC |
1
|
-11.908
|
2.95e-10
|
-2.663
|
| Metro_vs_SMC |
2
|
-26.633
|
1.65e-16
|
-5.955
|
| Metro_vs_SMC |
3
|
-34.297
|
1.49e-18
|
-7.669
|
| Metro_vs_SMC |
4
|
-106.624
|
7.4e-28
|
-23.842
|
| DEMetro_Z_vs_SMC |
0
|
-21.851
|
6.33e-15
|
-4.886
|
| DEMetro_Z_vs_SMC |
1
|
-26.036
|
2.51e-16
|
-5.822
|
| DEMetro_Z_vs_SMC |
2
|
-24.605
|
7.15e-16
|
-5.502
|
| DEMetro_Z_vs_SMC |
3
|
-24.892
|
5.77e-16
|
-5.566
|
| DEMetro_Z_vs_SMC |
4
|
-85.768
|
4.59e-26
|
-19.178
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.975 |
5.195 |
11.992 |
0.065 |
| HMC |
3.0 |
1.030 |
0.411 |
0.273 |
2.273 |
| HMC |
4.0 |
0.357 |
0.147 |
0.088 |
2.401 |
| HMC |
10.0 |
0.117 |
0.034 |
0.015 |
5.454 |
| HMC |
50.0 |
0.123 |
0.034 |
0.018 |
4.868 |
| SMC |
2.1 |
8538.520 |
5.195 |
11.992 |
711.610 |
| SMC |
3.0 |
377.751 |
0.411 |
0.273 |
1383.760 |
| SMC |
4.0 |
404.424 |
0.147 |
0.088 |
4616.389 |
| SMC |
10.0 |
255.347 |
0.034 |
0.015 |
16720.900 |
| SMC |
50.0 |
529.036 |
0.034 |
0.018 |
29098.775 |
| Metro |
2.1 |
8570.566 |
5.195 |
11.992 |
714.282 |
| Metro |
3.0 |
69.027 |
0.411 |
0.273 |
251.626 |
| Metro |
4.0 |
48.336 |
0.147 |
0.088 |
550.263 |
| Metro |
10.0 |
6.332 |
0.034 |
0.015 |
412.503 |
| Metro |
50.0 |
1.427 |
0.034 |
0.018 |
76.597 |
| DEMetro_Z |
2.1 |
2533.696 |
5.195 |
11.992 |
210.856 |
| DEMetro_Z |
3.0 |
114.964 |
0.411 |
0.273 |
420.084 |
| DEMetro_Z |
4.0 |
114.716 |
0.147 |
0.088 |
1308.248 |
| DEMetro_Z |
10.0 |
29.953 |
0.034 |
0.015 |
1959.442 |
| DEMetro_Z |
50.0 |
24.178 |
0.034 |
0.018 |
1328.110 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.135 |
5.53e-05 |
11.236 |
| HMC |
3.0 |
7.051 |
9.1e-07 |
14.728 |
| HMC |
4.0 |
8.148 |
9.41e-08 |
12.624 |
| HMC |
10.0 |
9.525 |
2.72e-09 |
7.674 |
| HMC |
50.0 |
6.477 |
2.05e-06 |
6.531 |
| SMC |
2.1 |
288.955 |
4.14e-36 |
2852.097 |
| SMC |
3.0 |
312.978 |
7.06e-37 |
1478.715 |
| SMC |
4.0 |
280.045 |
7.08e-36 |
2055.262 |
| SMC |
10.0 |
59.812 |
4.19e-23 |
1465.435 |
| SMC |
50.0 |
82.192 |
1.02e-25 |
2818.752 |
| Metro |
2.1 |
4.625 |
0.000185 |
1304.580 |
| Metro |
3.0 |
5.528 |
2.48e-05 |
345.171 |
| Metro |
4.0 |
7.861 |
2.17e-07 |
505.115 |
| Metro |
10.0 |
7.854 |
2.2e-07 |
164.873 |
| Metro |
50.0 |
7.234 |
7.2e-07 |
97.896 |
| DEMetro_Z |
2.1 |
26.864 |
1.41e-16 |
1690.077 |
| DEMetro_Z |
3.0 |
22.342 |
4.21e-15 |
791.769 |
| DEMetro_Z |
4.0 |
17.831 |
2.54e-13 |
1094.837 |
| DEMetro_Z |
10.0 |
15.425 |
3.36e-12 |
477.915 |
| DEMetro_Z |
50.0 |
14.087 |
1.65e-11 |
493.987 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-1.391
|
0.18
|
-0.311
|
| Metro_vs_DEMetro_Z |
1
|
-5.678
|
1.79e-05
|
-1.270
|
| Metro_vs_DEMetro_Z |
2
|
-6.369
|
4.14e-06
|
-1.424
|
| Metro_vs_DEMetro_Z |
3
|
-8.229
|
1.1e-07
|
-1.840
|
| Metro_vs_DEMetro_Z |
4
|
-10.040
|
4.94e-09
|
-2.245
|
| DEMetro_Z_vs_SMC |
0
|
-18.107
|
1.92e-13
|
-4.049
|
| DEMetro_Z_vs_SMC |
1
|
-18.822
|
9.57e-14
|
-4.209
|
| DEMetro_Z_vs_SMC |
2
|
-15.439
|
3.31e-12
|
-3.452
|
| DEMetro_Z_vs_SMC |
3
|
-20.851
|
1.49e-14
|
-4.662
|
| DEMetro_Z_vs_SMC |
4
|
-50.682
|
9.63e-22
|
-11.333
|
| HMC_vs_DEMetro_Z |
0
|
-26.657
|
1.63e-16
|
-5.961
|
| HMC_vs_DEMetro_Z |
1
|
-21.526
|
8.33e-15
|
-4.813
|
| HMC_vs_DEMetro_Z |
2
|
-17.607
|
3.19e-13
|
-3.937
|
| HMC_vs_DEMetro_Z |
3
|
-14.999
|
5.51e-12
|
-3.354
|
| HMC_vs_DEMetro_Z |
4
|
-13.936
|
1.99e-11
|
-3.116
|
| HMC_vs_Metro |
0
|
-4.579
|
0.000205
|
-1.024
|
| HMC_vs_Metro |
1
|
-5.385
|
3.39e-05
|
-1.204
|
| HMC_vs_Metro |
2
|
-7.635
|
3.33e-07
|
-1.707
|
| HMC_vs_Metro |
3
|
-7.487
|
4.42e-07
|
-1.674
|
| HMC_vs_Metro |
4
|
-6.649
|
2.33e-06
|
-1.487
|
| HMC_vs_SMC |
0
|
-289.258
|
4.36e-36
|
-64.680
|
| HMC_vs_SMC |
1
|
-283.460
|
6.41e-36
|
-63.383
|
| HMC_vs_SMC |
2
|
-266.503
|
2.07e-35
|
-59.592
|
| HMC_vs_SMC |
3
|
-59.461
|
4.72e-23
|
-13.296
|
| HMC_vs_SMC |
4
|
-81.690
|
1.16e-25
|
-18.266
|
| Metro_vs_SMC |
0
|
-5.475
|
2.79e-05
|
-1.224
|
| Metro_vs_SMC |
1
|
-18.295
|
1.6e-13
|
-4.091
|
| Metro_vs_SMC |
2
|
-24.606
|
7.14e-16
|
-5.502
|
| Metro_vs_SMC |
3
|
-41.094
|
5e-20
|
-9.189
|
| Metro_vs_SMC |
4
|
-66.964
|
4.98e-24
|
-14.974
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.396 |
0.104 |
0.026 |
11.236 |
| HMC |
3.0 |
0.200 |
0.056 |
0.010 |
14.728 |
| HMC |
4.0 |
0.133 |
0.040 |
0.007 |
12.624 |
| HMC |
10.0 |
0.088 |
0.028 |
0.008 |
7.674 |
| HMC |
50.0 |
0.067 |
0.025 |
0.006 |
6.531 |
| SMC |
2.1 |
74.102 |
0.104 |
0.026 |
2852.097 |
| SMC |
3.0 |
14.492 |
0.056 |
0.010 |
1478.715 |
| SMC |
4.0 |
15.119 |
0.040 |
0.007 |
2055.262 |
| SMC |
10.0 |
11.398 |
0.028 |
0.008 |
1465.435 |
| SMC |
50.0 |
17.944 |
0.025 |
0.006 |
2818.752 |
| Metro |
2.1 |
33.952 |
0.104 |
0.026 |
1304.580 |
| Metro |
3.0 |
3.426 |
0.056 |
0.010 |
345.171 |
| Metro |
4.0 |
3.746 |
0.040 |
0.007 |
505.115 |
| Metro |
10.0 |
1.307 |
0.028 |
0.008 |
164.873 |
| Metro |
50.0 |
0.648 |
0.025 |
0.006 |
97.896 |
| DEMetro_Z |
2.1 |
43.953 |
0.104 |
0.026 |
1690.077 |
| DEMetro_Z |
3.0 |
7.786 |
0.056 |
0.010 |
791.769 |
| DEMetro_Z |
4.0 |
8.073 |
0.040 |
0.007 |
1094.837 |
| DEMetro_Z |
10.0 |
3.736 |
0.028 |
0.008 |
477.915 |
| DEMetro_Z |
50.0 |
3.166 |
0.025 |
0.006 |
493.987 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.485 |
3.72e-07 |
14.131 |
| HMC |
3.0 |
6.523 |
2.59e-06 |
11.793 |
| HMC |
4.0 |
6.514 |
2.6e-06 |
11.160 |
| HMC |
10.0 |
9.200 |
7.07e-09 |
8.527 |
| HMC |
50.0 |
5.908 |
7.3e-06 |
5.929 |
| SMC |
2.1 |
136.386 |
7.95e-38 |
79.751 |
| SMC |
3.0 |
158.470 |
6.3e-40 |
90.426 |
| SMC |
4.0 |
189.834 |
2.74e-40 |
118.552 |
| SMC |
10.0 |
68.112 |
1.08e-24 |
129.832 |
| SMC |
50.0 |
77.487 |
5.37e-26 |
125.597 |
| Metro |
2.1 |
53.870 |
1.34e-22 |
117.658 |
| Metro |
3.0 |
13.172 |
5.16e-11 |
99.609 |
| Metro |
4.0 |
15.963 |
1.8e-12 |
148.664 |
| Metro |
10.0 |
9.771 |
7.55e-09 |
91.348 |
| Metro |
50.0 |
10.696 |
1.71e-09 |
62.884 |
| DEMetro_Z |
2.1 |
40.903 |
3.6e-20 |
116.485 |
| DEMetro_Z |
3.0 |
44.761 |
6.21e-21 |
122.066 |
| DEMetro_Z |
4.0 |
24.717 |
6.22e-16 |
164.602 |
| DEMetro_Z |
10.0 |
33.112 |
2.3e-18 |
122.273 |
| DEMetro_Z |
50.0 |
31.027 |
7.79e-18 |
113.450 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
12.980
|
6.81e-11
|
2.902
|
| DEMetro_Z_vs_SMC |
1
|
11.621
|
4.44e-10
|
2.599
|
| DEMetro_Z_vs_SMC |
2
|
6.985
|
1.18e-06
|
1.562
|
| DEMetro_Z_vs_SMC |
3
|
-1.635
|
0.119
|
-0.366
|
| DEMetro_Z_vs_SMC |
4
|
-3.177
|
0.00496
|
-0.710
|
| HMC_vs_Metro |
0
|
-45.609
|
7.04e-21
|
-10.198
|
| HMC_vs_Metro |
1
|
-12.340
|
1.61e-10
|
-2.759
|
| HMC_vs_Metro |
2
|
-14.777
|
7.16e-12
|
-3.304
|
| HMC_vs_Metro |
3
|
-8.811
|
3.88e-08
|
-1.970
|
| HMC_vs_Metro |
4
|
-9.526
|
1.14e-08
|
-2.130
|
| Metro_vs_DEMetro_Z |
0
|
0.310
|
0.76
|
0.069
|
| Metro_vs_DEMetro_Z |
1
|
-2.603
|
0.0175
|
-0.582
|
| Metro_vs_DEMetro_Z |
2
|
-1.647
|
0.116
|
-0.368
|
| Metro_vs_DEMetro_Z |
3
|
-2.961
|
0.00802
|
-0.662
|
| Metro_vs_DEMetro_Z |
4
|
-7.104
|
9.34e-07
|
-1.588
|
| HMC_vs_SMC |
0
|
-31.678
|
6.56e-18
|
-7.083
|
| HMC_vs_SMC |
1
|
-40.761
|
5.83e-20
|
-9.114
|
| HMC_vs_SMC |
2
|
-57.604
|
8.59e-23
|
-12.881
|
| HMC_vs_SMC |
3
|
-58.850
|
5.73e-23
|
-13.159
|
| HMC_vs_SMC |
4
|
-62.843
|
1.66e-23
|
-14.052
|
| Metro_vs_SMC |
0
|
15.508
|
3.06e-12
|
3.468
|
| Metro_vs_SMC |
1
|
1.181
|
0.252
|
0.264
|
| Metro_vs_SMC |
2
|
3.205
|
0.00466
|
0.717
|
| Metro_vs_SMC |
3
|
-4.111
|
0.000595
|
-0.919
|
| Metro_vs_SMC |
4
|
-9.497
|
1.2e-08
|
-2.124
|
| HMC_vs_DEMetro_Z |
0
|
-30.433
|
1.39e-17
|
-6.805
|
| HMC_vs_DEMetro_Z |
1
|
-35.301
|
8.66e-19
|
-7.894
|
| HMC_vs_DEMetro_Z |
2
|
-23.587
|
1.56e-15
|
-5.274
|
| HMC_vs_DEMetro_Z |
3
|
-29.266
|
2.87e-17
|
-6.544
|
| HMC_vs_DEMetro_Z |
4
|
-32.132
|
5.03e-18
|
-7.185
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.094 |
0.017 |
0.005 |
14.131 |
| HMC |
3.0 |
0.069 |
0.015 |
0.005 |
11.793 |
| HMC |
4.0 |
0.054 |
0.014 |
0.004 |
11.160 |
| HMC |
10.0 |
0.052 |
0.013 |
0.005 |
8.527 |
| HMC |
50.0 |
0.044 |
0.014 |
0.005 |
5.929 |
| SMC |
2.1 |
0.452 |
0.017 |
0.005 |
79.751 |
| SMC |
3.0 |
0.431 |
0.015 |
0.005 |
90.426 |
| SMC |
4.0 |
0.439 |
0.014 |
0.004 |
118.552 |
| SMC |
10.0 |
0.610 |
0.013 |
0.005 |
129.832 |
| SMC |
50.0 |
0.649 |
0.014 |
0.005 |
125.597 |
| Metro |
2.1 |
0.658 |
0.017 |
0.005 |
117.658 |
| Metro |
3.0 |
0.473 |
0.015 |
0.005 |
99.609 |
| Metro |
4.0 |
0.547 |
0.014 |
0.004 |
148.664 |
| Metro |
10.0 |
0.433 |
0.013 |
0.005 |
91.348 |
| Metro |
50.0 |
0.332 |
0.014 |
0.005 |
62.884 |
| DEMetro_Z |
2.1 |
0.652 |
0.017 |
0.005 |
116.485 |
| DEMetro_Z |
3.0 |
0.576 |
0.015 |
0.005 |
122.066 |
| DEMetro_Z |
4.0 |
0.604 |
0.014 |
0.004 |
164.602 |
| DEMetro_Z |
10.0 |
0.576 |
0.013 |
0.005 |
122.273 |
| DEMetro_Z |
50.0 |
0.588 |
0.014 |
0.005 |
113.450 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.154 |
0.0431 |
2.216 |
| HMC |
3.0 |
3.097 |
0.00583 |
6.951 |
| HMC |
4.0 |
4.792 |
0.000122 |
12.133 |
| HMC |
10.0 |
4.946 |
7.71e-05 |
6.712 |
| HMC |
50.0 |
3.912 |
0.000889 |
6.771 |
| SMC |
2.1 |
45.203 |
8.2e-21 |
678.647 |
| SMC |
3.0 |
12.414 |
1.09e-10 |
26.160 |
| SMC |
4.0 |
7.646 |
3.23e-07 |
63.664 |
| SMC |
10.0 |
5.385 |
3.38e-05 |
53.247 |
| SMC |
50.0 |
18.684 |
1.09e-13 |
424.228 |
| Metro |
2.1 |
6.190 |
6.01e-06 |
481.010 |
| Metro |
3.0 |
4.023 |
0.000728 |
226.850 |
| Metro |
4.0 |
4.562 |
0.000213 |
156.847 |
| Metro |
10.0 |
3.772 |
0.00129 |
124.463 |
| Metro |
50.0 |
4.405 |
0.000304 |
38.274 |
| DEMetro_Z |
2.1 |
7.503 |
4.29e-07 |
923.588 |
| DEMetro_Z |
3.0 |
6.607 |
2.53e-06 |
421.732 |
| DEMetro_Z |
4.0 |
4.249 |
0.000434 |
440.191 |
| DEMetro_Z |
10.0 |
4.339 |
0.000353 |
282.374 |
| DEMetro_Z |
50.0 |
5.133 |
5.91e-05 |
352.496 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-7.483
|
4.45e-07
|
-1.673
|
| HMC_vs_DEMetro_Z |
1
|
-6.566
|
2.76e-06
|
-1.468
|
| HMC_vs_DEMetro_Z |
2
|
-4.163
|
0.000528
|
-0.931
|
| HMC_vs_DEMetro_Z |
3
|
-4.235
|
0.000448
|
-0.947
|
| HMC_vs_DEMetro_Z |
4
|
-4.993
|
8.07e-05
|
-1.117
|
| Metro_vs_SMC |
0
|
-2.603
|
0.0175
|
-0.582
|
| Metro_vs_SMC |
1
|
3.572
|
0.00204
|
0.799
|
| Metro_vs_SMC |
2
|
2.560
|
0.0191
|
0.572
|
| Metro_vs_SMC |
3
|
2.079
|
0.0514
|
0.465
|
| Metro_vs_SMC |
4
|
-14.531
|
9.61e-12
|
-3.249
|
| Metro_vs_DEMetro_Z |
0
|
-3.514
|
0.00232
|
-0.786
|
| Metro_vs_DEMetro_Z |
1
|
-3.374
|
0.00319
|
-0.754
|
| Metro_vs_DEMetro_Z |
2
|
-2.529
|
0.0204
|
-0.566
|
| Metro_vs_DEMetro_Z |
3
|
-2.191
|
0.0411
|
-0.490
|
| Metro_vs_DEMetro_Z |
4
|
-4.789
|
0.000128
|
-1.071
|
| HMC_vs_Metro |
0
|
-6.151
|
6.52e-06
|
-1.375
|
| HMC_vs_Metro |
1
|
-4.021
|
0.000729
|
-0.899
|
| HMC_vs_Metro |
2
|
-4.232
|
0.000451
|
-0.946
|
| HMC_vs_Metro |
3
|
-3.553
|
0.00212
|
-0.794
|
| HMC_vs_Metro |
4
|
-3.575
|
0.00202
|
-0.799
|
| HMC_vs_SMC |
0
|
-45.529
|
7.27e-21
|
-10.181
|
| HMC_vs_SMC |
1
|
-5.955
|
9.88e-06
|
-1.332
|
| HMC_vs_SMC |
2
|
-6.197
|
5.92e-06
|
-1.386
|
| HMC_vs_SMC |
3
|
-4.812
|
0.000121
|
-1.076
|
| HMC_vs_SMC |
4
|
-18.105
|
1.93e-13
|
-4.048
|
| DEMetro_Z_vs_SMC |
0
|
1.925
|
0.0694
|
0.430
|
| DEMetro_Z_vs_SMC |
1
|
6.241
|
5.41e-06
|
1.395
|
| DEMetro_Z_vs_SMC |
2
|
3.558
|
0.0021
|
0.796
|
| DEMetro_Z_vs_SMC |
3
|
3.337
|
0.00346
|
0.746
|
| DEMetro_Z_vs_SMC |
4
|
-1.004
|
0.328
|
-0.225
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.147 |
0.069 |
0.035 |
2.216 |
| HMC |
3.0 |
0.164 |
0.032 |
0.019 |
6.951 |
| HMC |
4.0 |
0.202 |
0.026 |
0.015 |
12.133 |
| HMC |
10.0 |
0.113 |
0.021 |
0.014 |
6.712 |
| HMC |
50.0 |
0.099 |
0.019 |
0.012 |
6.771 |
| SMC |
2.1 |
23.892 |
0.069 |
0.035 |
678.647 |
| SMC |
3.0 |
0.527 |
0.032 |
0.019 |
26.160 |
| SMC |
4.0 |
0.949 |
0.026 |
0.015 |
63.664 |
| SMC |
10.0 |
0.755 |
0.021 |
0.014 |
53.247 |
| SMC |
50.0 |
5.025 |
0.019 |
0.012 |
424.228 |
| Metro |
2.1 |
16.954 |
0.069 |
0.035 |
481.010 |
| Metro |
3.0 |
4.317 |
0.032 |
0.019 |
226.850 |
| Metro |
4.0 |
2.301 |
0.026 |
0.015 |
156.847 |
| Metro |
10.0 |
1.737 |
0.021 |
0.014 |
124.463 |
| Metro |
50.0 |
0.470 |
0.019 |
0.012 |
38.274 |
| DEMetro_Z |
2.1 |
32.490 |
0.069 |
0.035 |
923.588 |
| DEMetro_Z |
3.0 |
7.999 |
0.032 |
0.019 |
421.732 |
| DEMetro_Z |
4.0 |
6.410 |
0.026 |
0.015 |
440.191 |
| DEMetro_Z |
10.0 |
3.915 |
0.021 |
0.014 |
282.374 |
| DEMetro_Z |
50.0 |
4.178 |
0.019 |
0.012 |
352.496 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.139 |
0.891 |
0.034 |
| HMC |
3.0 |
1.744 |
0.0973 |
6.223 |
| HMC |
4.0 |
3.168 |
0.00495 |
6.190 |
| HMC |
10.0 |
4.540 |
0.000206 |
7.493 |
| HMC |
50.0 |
3.582 |
0.00176 |
3.578 |
| SMC |
2.1 |
205.575 |
1.77e-33 |
751.836 |
| SMC |
3.0 |
221.164 |
6.16e-34 |
1474.317 |
| SMC |
4.0 |
134.404 |
9.1e-30 |
4988.564 |
| SMC |
10.0 |
139.009 |
4.82e-30 |
26405.446 |
| SMC |
50.0 |
101.698 |
1.81e-27 |
31105.324 |
| Metro |
2.1 |
1.734 |
0.0992 |
87.843 |
| Metro |
3.0 |
1.236 |
0.231 |
176.870 |
| Metro |
4.0 |
1.694 |
0.107 |
96.537 |
| Metro |
10.0 |
2.477 |
0.0228 |
175.957 |
| Metro |
50.0 |
4.318 |
0.000369 |
28.844 |
| DEMetro_Z |
2.1 |
13.773 |
2.23e-11 |
54.369 |
| DEMetro_Z |
3.0 |
10.778 |
1.52e-09 |
73.256 |
| DEMetro_Z |
4.0 |
9.140 |
2.19e-08 |
220.699 |
| DEMetro_Z |
10.0 |
11.044 |
1.04e-09 |
209.484 |
| DEMetro_Z |
50.0 |
4.314 |
0.000374 |
89.004 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-206.220
|
2.7e-33
|
-46.112
|
| HMC_vs_SMC |
1
|
-195.611
|
7.35e-33
|
-43.740
|
| HMC_vs_SMC |
2
|
-132.551
|
1.19e-29
|
-29.639
|
| HMC_vs_SMC |
3
|
-138.873
|
4.91e-30
|
-31.053
|
| HMC_vs_SMC |
4
|
-101.558
|
1.86e-27
|
-22.709
|
| Metro_vs_DEMetro_Z |
0
|
0.660
|
0.517
|
0.148
|
| Metro_vs_DEMetro_Z |
1
|
0.734
|
0.472
|
0.164
|
| Metro_vs_DEMetro_Z |
2
|
-1.893
|
0.0736
|
-0.423
|
| Metro_vs_DEMetro_Z |
3
|
-0.484
|
0.634
|
-0.108
|
| Metro_vs_DEMetro_Z |
4
|
-2.584
|
0.0182
|
-0.578
|
| HMC_vs_Metro |
0
|
-1.733
|
0.0993
|
-0.387
|
| HMC_vs_Metro |
1
|
-1.221
|
0.237
|
-0.273
|
| HMC_vs_Metro |
2
|
-1.578
|
0.131
|
-0.353
|
| HMC_vs_Metro |
3
|
-2.362
|
0.029
|
-0.528
|
| HMC_vs_Metro |
4
|
-3.723
|
0.00144
|
-0.833
|
| HMC_vs_DEMetro_Z |
0
|
-13.738
|
2.56e-11
|
-3.072
|
| HMC_vs_DEMetro_Z |
1
|
-10.507
|
2.36e-09
|
-2.349
|
| HMC_vs_DEMetro_Z |
2
|
-8.998
|
2.8e-08
|
-2.012
|
| HMC_vs_DEMetro_Z |
3
|
-10.437
|
2.63e-09
|
-2.334
|
| HMC_vs_DEMetro_Z |
4
|
-4.130
|
0.000569
|
-0.924
|
| Metro_vs_SMC |
0
|
-13.122
|
5.65e-11
|
-2.934
|
| Metro_vs_SMC |
1
|
-9.069
|
2.48e-08
|
-2.028
|
| Metro_vs_SMC |
2
|
-79.456
|
1.95e-25
|
-17.767
|
| Metro_vs_SMC |
3
|
-146.364
|
1.81e-30
|
-32.728
|
| Metro_vs_SMC |
4
|
-101.339
|
1.94e-27
|
-22.660
|
| DEMetro_Z_vs_SMC |
0
|
-157.766
|
4.36e-31
|
-35.278
|
| DEMetro_Z_vs_SMC |
1
|
-162.516
|
2.48e-31
|
-36.340
|
| DEMetro_Z_vs_SMC |
2
|
-106.688
|
7.32e-28
|
-23.856
|
| DEMetro_Z_vs_SMC |
3
|
-140.819
|
3.77e-30
|
-31.488
|
| DEMetro_Z_vs_SMC |
4
|
-100.837
|
2.13e-27
|
-22.548
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.605 |
5.195 |
11.992 |
0.034 |
| HMC |
3.0 |
2.107 |
0.411 |
0.273 |
6.223 |
| HMC |
4.0 |
0.689 |
0.147 |
0.088 |
6.190 |
| HMC |
10.0 |
0.148 |
0.034 |
0.015 |
7.493 |
| HMC |
50.0 |
0.099 |
0.034 |
0.018 |
3.578 |
| SMC |
2.1 |
9020.891 |
5.195 |
11.992 |
751.836 |
| SMC |
3.0 |
402.445 |
0.411 |
0.273 |
1474.317 |
| SMC |
4.0 |
437.017 |
0.147 |
0.088 |
4988.564 |
| SMC |
10.0 |
403.222 |
0.034 |
0.015 |
26405.446 |
| SMC |
50.0 |
565.514 |
0.034 |
0.018 |
31105.324 |
| Metro |
2.1 |
1058.567 |
5.195 |
11.992 |
87.843 |
| Metro |
3.0 |
48.642 |
0.411 |
0.273 |
176.870 |
| Metro |
4.0 |
8.601 |
0.147 |
0.088 |
96.537 |
| Metro |
10.0 |
2.721 |
0.034 |
0.015 |
175.957 |
| Metro |
50.0 |
0.558 |
0.034 |
0.018 |
28.844 |
| DEMetro_Z |
2.1 |
657.163 |
5.195 |
11.992 |
54.369 |
| DEMetro_Z |
3.0 |
20.387 |
0.411 |
0.273 |
73.256 |
| DEMetro_Z |
4.0 |
19.474 |
0.147 |
0.088 |
220.699 |
| DEMetro_Z |
10.0 |
3.232 |
0.034 |
0.015 |
209.484 |
| DEMetro_Z |
50.0 |
1.652 |
0.034 |
0.018 |
89.004 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
6.381 |
3.05e-06 |
8.311 |
| HMC |
3.0 |
4.873 |
0.000103 |
15.145 |
| HMC |
4.0 |
5.676 |
1.75e-05 |
20.573 |
| HMC |
10.0 |
6.308 |
3.97e-06 |
10.461 |
| HMC |
50.0 |
4.705 |
0.000147 |
10.903 |
| SMC |
2.1 |
228.586 |
3.66e-34 |
2902.725 |
| SMC |
3.0 |
247.518 |
7.04e-35 |
1521.573 |
| SMC |
4.0 |
181.013 |
3.07e-32 |
2113.543 |
| SMC |
10.0 |
105.896 |
8.29e-28 |
1902.547 |
| SMC |
50.0 |
103.544 |
1.28e-27 |
2937.294 |
| Metro |
2.1 |
6.165 |
6.34e-06 |
565.941 |
| Metro |
3.0 |
4.148 |
0.000547 |
369.132 |
| Metro |
4.0 |
4.696 |
0.000157 |
263.806 |
| Metro |
10.0 |
3.832 |
0.00113 |
184.059 |
| Metro |
50.0 |
5.165 |
5.49e-05 |
62.974 |
| DEMetro_Z |
2.1 |
11.778 |
3.55e-10 |
1263.176 |
| DEMetro_Z |
3.0 |
7.710 |
2.89e-07 |
754.191 |
| DEMetro_Z |
4.0 |
5.238 |
4.68e-05 |
814.335 |
| DEMetro_Z |
10.0 |
4.740 |
0.000143 |
435.807 |
| DEMetro_Z |
50.0 |
5.406 |
3.24e-05 |
546.338 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-5.983
|
9.32e-06
|
-1.338
|
| Metro_vs_DEMetro_Z |
1
|
-4.366
|
0.000332
|
-0.976
|
| Metro_vs_DEMetro_Z |
2
|
-3.255
|
0.00417
|
-0.728
|
| Metro_vs_DEMetro_Z |
3
|
-2.430
|
0.0252
|
-0.543
|
| Metro_vs_DEMetro_Z |
4
|
-5.001
|
7.94e-05
|
-1.118
|
| DEMetro_Z_vs_SMC |
0
|
-15.140
|
4.67e-12
|
-3.385
|
| DEMetro_Z_vs_SMC |
1
|
-7.826
|
2.32e-07
|
-1.750
|
| DEMetro_Z_vs_SMC |
2
|
-8.046
|
1.54e-07
|
-1.799
|
| DEMetro_Z_vs_SMC |
3
|
-15.469
|
3.2e-12
|
-3.459
|
| DEMetro_Z_vs_SMC |
4
|
-20.581
|
1.89e-14
|
-4.602
|
| HMC_vs_DEMetro_Z |
0
|
-11.670
|
4.14e-10
|
-2.610
|
| HMC_vs_DEMetro_Z |
1
|
-7.658
|
3.19e-07
|
-1.712
|
| HMC_vs_DEMetro_Z |
2
|
-5.144
|
5.77e-05
|
-1.150
|
| HMC_vs_DEMetro_Z |
3
|
-4.619
|
0.000187
|
-1.033
|
| HMC_vs_DEMetro_Z |
4
|
-5.270
|
4.36e-05
|
-1.178
|
| HMC_vs_Metro |
0
|
-6.045
|
8.16e-06
|
-1.352
|
| HMC_vs_Metro |
1
|
-4.081
|
0.000636
|
-0.913
|
| HMC_vs_Metro |
2
|
-4.346
|
0.000348
|
-0.972
|
| HMC_vs_Metro |
3
|
-3.599
|
0.00191
|
-0.805
|
| HMC_vs_Metro |
4
|
-4.249
|
0.000434
|
-0.950
|
| HMC_vs_SMC |
0
|
-229.215
|
3.62e-34
|
-51.254
|
| HMC_vs_SMC |
1
|
-214.092
|
1.32e-33
|
-47.872
|
| HMC_vs_SMC |
2
|
-169.732
|
1.09e-31
|
-37.953
|
| HMC_vs_SMC |
3
|
-110.031
|
4.07e-28
|
-24.604
|
| HMC_vs_SMC |
4
|
-102.123
|
1.68e-27
|
-22.835
|
| Metro_vs_SMC |
0
|
-26.765
|
1.51e-16
|
-5.985
|
| Metro_vs_SMC |
1
|
-12.787
|
8.79e-11
|
-2.859
|
| Metro_vs_SMC |
2
|
-32.689
|
3.65e-18
|
-7.310
|
| Metro_vs_SMC |
3
|
-35.717
|
6.96e-19
|
-7.986
|
| Metro_vs_SMC |
4
|
-87.504
|
3.14e-26
|
-19.567
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.320 |
0.104 |
0.026 |
8.311 |
| HMC |
3.0 |
0.204 |
0.056 |
0.010 |
15.145 |
| HMC |
4.0 |
0.191 |
0.040 |
0.007 |
20.573 |
| HMC |
10.0 |
0.109 |
0.028 |
0.008 |
10.461 |
| HMC |
50.0 |
0.095 |
0.025 |
0.006 |
10.903 |
| SMC |
2.1 |
75.416 |
0.104 |
0.026 |
2902.725 |
| SMC |
3.0 |
14.910 |
0.056 |
0.010 |
1521.573 |
| SMC |
4.0 |
15.547 |
0.040 |
0.007 |
2113.543 |
| SMC |
10.0 |
14.790 |
0.028 |
0.008 |
1902.547 |
| SMC |
50.0 |
18.697 |
0.025 |
0.006 |
2937.294 |
| Metro |
2.1 |
14.788 |
0.104 |
0.026 |
565.941 |
| Metro |
3.0 |
3.660 |
0.056 |
0.010 |
369.132 |
| Metro |
4.0 |
1.976 |
0.040 |
0.007 |
263.806 |
| Metro |
10.0 |
1.456 |
0.028 |
0.008 |
184.059 |
| Metro |
50.0 |
0.426 |
0.025 |
0.006 |
62.974 |
| DEMetro_Z |
2.1 |
32.877 |
0.104 |
0.026 |
1263.176 |
| DEMetro_Z |
3.0 |
7.419 |
0.056 |
0.010 |
754.191 |
| DEMetro_Z |
4.0 |
6.015 |
0.040 |
0.007 |
814.335 |
| DEMetro_Z |
10.0 |
3.410 |
0.028 |
0.008 |
435.807 |
| DEMetro_Z |
50.0 |
3.498 |
0.025 |
0.006 |
546.338 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
8.743 |
2.33e-08 |
9.939 |
| HMC |
3.0 |
10.609 |
4.43e-10 |
8.981 |
| HMC |
4.0 |
6.721 |
1.77e-06 |
13.463 |
| HMC |
10.0 |
7.531 |
2.72e-07 |
9.496 |
| HMC |
50.0 |
5.039 |
6.49e-05 |
7.971 |
| SMC |
2.1 |
97.730 |
2.79e-30 |
83.473 |
| SMC |
3.0 |
105.945 |
1.06e-30 |
95.454 |
| SMC |
4.0 |
90.356 |
1.25e-27 |
124.487 |
| SMC |
10.0 |
72.695 |
3.15e-25 |
140.363 |
| SMC |
50.0 |
99.260 |
1.08e-28 |
124.531 |
| Metro |
2.1 |
20.554 |
1.84e-14 |
129.405 |
| Metro |
3.0 |
12.670 |
1.02e-10 |
137.012 |
| Metro |
4.0 |
10.855 |
1.37e-09 |
149.095 |
| Metro |
10.0 |
8.306 |
9.51e-08 |
96.213 |
| Metro |
50.0 |
7.611 |
3.42e-07 |
44.993 |
| DEMetro_Z |
2.1 |
20.569 |
1.82e-14 |
134.959 |
| DEMetro_Z |
3.0 |
15.804 |
2.16e-12 |
167.826 |
| DEMetro_Z |
4.0 |
14.405 |
1.11e-11 |
190.936 |
| DEMetro_Z |
10.0 |
11.619 |
4.43e-10 |
160.346 |
| DEMetro_Z |
50.0 |
13.388 |
3.96e-11 |
162.428 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.883
|
2.09e-07
|
1.763
|
| DEMetro_Z_vs_SMC |
1
|
6.745
|
1.91e-06
|
1.508
|
| DEMetro_Z_vs_SMC |
2
|
5.138
|
5.85e-05
|
1.149
|
| DEMetro_Z_vs_SMC |
3
|
1.519
|
0.145
|
0.340
|
| DEMetro_Z_vs_SMC |
4
|
3.207
|
0.00464
|
0.717
|
| HMC_vs_Metro |
0
|
-18.805
|
9.73e-14
|
-4.205
|
| HMC_vs_Metro |
1
|
-11.877
|
3.08e-10
|
-2.656
|
| HMC_vs_Metro |
2
|
-9.655
|
9.24e-09
|
-2.159
|
| HMC_vs_Metro |
3
|
-7.570
|
3.77e-07
|
-1.693
|
| HMC_vs_Metro |
4
|
-6.368
|
4.15e-06
|
-1.424
|
| Metro_vs_DEMetro_Z |
0
|
-0.677
|
0.507
|
-0.151
|
| Metro_vs_DEMetro_Z |
1
|
-2.893
|
0.00932
|
-0.647
|
| Metro_vs_DEMetro_Z |
2
|
-2.061
|
0.0533
|
-0.461
|
| Metro_vs_DEMetro_Z |
3
|
-3.840
|
0.0011
|
-0.859
|
| Metro_vs_DEMetro_Z |
4
|
-8.614
|
5.5e-08
|
-1.926
|
| HMC_vs_SMC |
0
|
-49.022
|
1.81e-21
|
-10.962
|
| HMC_vs_SMC |
1
|
-72.405
|
1.14e-24
|
-16.190
|
| HMC_vs_SMC |
2
|
-44.804
|
9.84e-21
|
-10.019
|
| HMC_vs_SMC |
3
|
-60.829
|
3.07e-23
|
-13.602
|
| HMC_vs_SMC |
4
|
-50.202
|
1.15e-21
|
-11.226
|
| Metro_vs_SMC |
0
|
7.582
|
3.69e-07
|
1.695
|
| Metro_vs_SMC |
1
|
3.858
|
0.00106
|
0.863
|
| Metro_vs_SMC |
2
|
1.722
|
0.101
|
0.385
|
| Metro_vs_SMC |
3
|
-3.659
|
0.00167
|
-0.818
|
| Metro_vs_SMC |
4
|
-13.087
|
5.91e-11
|
-2.926
|
| HMC_vs_DEMetro_Z |
0
|
-18.490
|
1.32e-13
|
-4.135
|
| HMC_vs_DEMetro_Z |
1
|
-15.050
|
5.19e-12
|
-3.365
|
| HMC_vs_DEMetro_Z |
2
|
-12.904
|
7.52e-11
|
-2.885
|
| HMC_vs_DEMetro_Z |
3
|
-10.905
|
1.28e-09
|
-2.438
|
| HMC_vs_DEMetro_Z |
4
|
-12.325
|
1.65e-10
|
-2.756
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.071 |
0.017 |
0.005 |
9.939 |
| HMC |
3.0 |
0.056 |
0.015 |
0.005 |
8.981 |
| HMC |
4.0 |
0.062 |
0.014 |
0.004 |
13.463 |
| HMC |
10.0 |
0.057 |
0.013 |
0.005 |
9.496 |
| HMC |
50.0 |
0.054 |
0.014 |
0.005 |
7.971 |
| SMC |
2.1 |
0.472 |
0.017 |
0.005 |
83.473 |
| SMC |
3.0 |
0.454 |
0.015 |
0.005 |
95.454 |
| SMC |
4.0 |
0.460 |
0.014 |
0.004 |
124.487 |
| SMC |
10.0 |
0.659 |
0.013 |
0.005 |
140.363 |
| SMC |
50.0 |
0.644 |
0.014 |
0.005 |
124.531 |
| Metro |
2.1 |
0.722 |
0.017 |
0.005 |
129.405 |
| Metro |
3.0 |
0.645 |
0.015 |
0.005 |
137.012 |
| Metro |
4.0 |
0.549 |
0.014 |
0.004 |
149.095 |
| Metro |
10.0 |
0.456 |
0.013 |
0.005 |
96.213 |
| Metro |
50.0 |
0.242 |
0.014 |
0.005 |
44.993 |
| DEMetro_Z |
2.1 |
0.753 |
0.017 |
0.005 |
134.959 |
| DEMetro_Z |
3.0 |
0.787 |
0.015 |
0.005 |
167.826 |
| DEMetro_Z |
4.0 |
0.699 |
0.014 |
0.004 |
190.936 |
| DEMetro_Z |
10.0 |
0.751 |
0.013 |
0.005 |
160.346 |
| DEMetro_Z |
50.0 |
0.835 |
0.014 |
0.005 |
162.428 |
Runtime
Runtime (scatter)
Ess
Ess Per Sec
R Hat
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain